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This is to certify that the

dissertation entitled
High Pressure Multi-Phase Equilibrium

of Carbon Dioxide with Organic Solids
in Binary and Ternary Systems

presented by

Gary Leon White

has been accepted towards fulfillment
of the requirements for

Ph.D. (kgmfin Chemical Engineering

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MSU Is An Affirmative Action/Equal Opportunity Institution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HIGH PRESSURE NULTI-PEASE EQUILIBRIUM
OF CARBON DIOXIDE 'ITE ORGANIC SOLIDS
IN BINARY AND TERNAR! SYSTEMS

BY
Gary Leon White

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1991

ABSTRACT

HIGH PRESSURE NULTI-PEASE EQUILIBRIUM OF CARBON DIOXIDE WITH
ORGANIC SOLIDS IN BINARY AND TERNARY SYSTEMS

BY
Gary Leon White

To test and improve predictive models for
multi-component systems, the loci of the phase boundaries
must be known. Such data for systems involving solids in
contact with supercritical fluids are still relatively
scarce. The objective of this work is to address that
shortage by acquiring new data from equilibrium measurements
in new systems and by modeling the observed phase behavior
using an equation of state.

An apparatus capable of providing phase equilibria data
for solid/SCF systems was designed and constructed. The
system consisted of a view cell to permit visual observation
of the phase behavior, a mechanism for sampling fluid phases
within the cell, and the equipment to control the pressure
and temperature in the cell. P-T-v-x-y data for the
coz+naphtha1ene system and P-T data for the C02+phenanthrene
system were measured along the SLV lines. P-T data were
obtained along the SSLV lines for the C02+naphthalene+r
ternary systems where the third component 7 = biphenyl,
phenanthrene, acenaphthene, or anthracene. Seven sets of
P-T-v-x-y data were obtained in the three phase regions of

the C02+naphthalene+biphenyl ternary system. As expected,

the binary systems studied exhibit melting point depressions
of the solids along the SUV line with temperature minimums
before terminating in upper critical end points. The phase
behavior of the C02+naphthalene+biphenyl and
C02+naphthalene+phenanthrene systems was different than
expected. Both exhibit eutectic melting point depressions
along their respective SSLV lines, but each intersects an
invariant point of undetermined type at a pressure much
lower than the upper critical end points of the constituent
solid/supercritical fluid binaries.

The data were used to test a modification of the
Peng-Robinson equation of state to determine if improving
the volume predictions for the pure components could also
improve the phase equilibrium predictions for mixtures of
these components. The results of the modeling indicate that
improving the predictions of the pure component volumes by
volume translations can sometimes improve the equilibrium
phase predictions for mixtures. The improvement is most

dramatic when the translations are largest.

To Sunshine

iv

ACKNOWLEDGMENTS

I wish to thank Dr. Carl T. Lira for the considerable
time and effort he has spent teaching me and advising me on
this project. I am especially appreciative of his patience
when the work was going slow or when family duties diverted
my attention temporarily from research.

I also wish to thank Dr. Victoria McGuffin and her
students for helping me resolve difficulties in the GC
analysis necessary for this work.

Partial support for this work by NSF Grant No. CBT10705
is gratefully acknowledged.

I would like to thank the Michigan State University and
the Gerstacker Foundation for their financial support during
this work.

I am thankful to my parents for their emotional support
as well as for loaning me the funds to support myself and my
family during my last term at MSU.

Most of all I want to thank my wife Kathy who has
endured 7 1/2 years of married student life while I

completed three college degrees.

TABLE OF CONTENTS

LIST OP TABLES

LIST OF FIGURES

CHAPTER 1:

CHAPTER 2:

CHAPTER 3:

CHAPTER 4:

CHAPTER 5:

INTRODUCTION . . . . . . . . . .

Phase Diagrams for Supercritical

Fluid-Solute mixtures . . . . . .
Historical Perspective . . . . .
Experimental Studies of Solid-SC!
View Cells . . . . . . . . . . .
Composition Determinations . . .
EXPERIMENTAL APPARATUS . . . . .
View Cell . . . . . . . . . . . .
Temperature Control . . . . . . .
Pressure Control . . . . . . . .
EXPERIMENTAL PROCEDURE . . . . .
Melting Point Curve Determination
Sampling . . . . . . . . . . . .
Composition Analysis . . . . . .
Materials . . . . . . . . . . . .
EXPERIMENTAL RESULTS . . . . . .
melting point experiments . . . .

Composition measurements . . . .

vi

BACKGROUND ON MULTI-PHASE EQUILIBRIUM . .

viii

ix

14
14
19
21
24
24
26
26
30
30
36
47
47
49
49

52

vii
CHAPTER 6: PREDICTIVE MODELING . . . . . . . . . . . . 58
Phase Equilibrium . . . . . . . . . . . . . 60
Solid Pugacities . . . . . . . . . . . . . 61
Liquid Pugacities . . . . . . . . . . . . . 62
Vapor or Supercritical Phase Pugacities . . 64
Pong-Robinson Equation of State . . . . . . 66
Translated Pang-Robinson Equation of State 67
Calculations and Comparison of Results . . 69

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS . . . . . . 83

Conclusions . . . . . . . . . . . . . . . . 83
Recommendations . . . . . . . . . . . . . . 86
APPENDICES
APPENDIX A: GC CALIBRATION . . . . . . . . . . . . . . 91

APPENDIX B: SAMPLE LOOP VOLUME DETERMINATIONS . . . . . 94
APPENDIX C: ITERATION SCHEME FOR SLV AND SSLV LINE
DETERMINATIONS . . . . . . . . . . . . . . 96
APPENDIX D: COMPUTER CODE FOR CALCULATING SLV AND SSLV LINES
. . . . . . . . . . . . . . . . . . . . . 99
APPENDIX E: ITERATION SCHEME FOR ISOTHERMAL SLV LINE
DETERMINATIONS IN TERNARY SYSTEMS . . . . 124
APPENDIX F: COMPUTER CODE FOR CALCULATING ISOTHERMAL SLV
LINES IN TERNARY SYSTEMS . . . . . . . . 128
APPENDIX G: EQUATION OF STATE PARAMETER DETERMINATIONS 138
APPENDIX H: RAW COMPOSITION DATA . . . . . . . . . . 146

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . 155

Table

Table
Table
Table

Table

Table

Table

Table

Table

Table

2.1

2.2

4.1

5.1

5.2

6.1

B.1

LIST OF TABLES

Previously Investigated Type P SCP + Solid
Systems . . . . . . . . . . . . . . . . . . . 17
Ternary Systems . . . . . . . . . . . . . . . 19
Purity of Materials . . . . . . . . . . . . . 48
Experimental Pressure-Temperature Data Along the
SLV and SSEV Equilibrium Lines for 6
coz+nydrocarbon Systems . . . . . . . . . . . 50
P-T-v-x-y Data for the C02+Naphthalene System.53
P-T-v-x-y Data for the coz+Naphthalene+Eiphenyl
System. . . . . . . . . . . . . . . . . . . . 53
Pure Component Triple Points . . . . . . . . 75
Binary Eutectic Temperatures . . . . . . . . 75

Data for volume determination of sample loop 1

O O O O O O O O O O O O O O O O O O O O O O 95

O O O O O O O O O O O O O O O O O O O O O O 95

viii

Figure
Figure

Figure

Figure

Figure

Figure

Figure
Figure

Figure

Figure
Figure
Figure

Figure

Figure

4.3

4.4

5.1

LIST OF FIGURES

Six types of binary fluid phase behavior. . . 7
Type F fluid phase diagram. . . . . . . . . . 8
P-T traces in a ternary system with

discontinuous critical locus. . . . . . . . . 11
Ternary composition diagram at fixed pressure

and temperature. . . . . . . . . . . . 13

Cross-sectional diagram of the view cell. . . 25

Constant temperature bath. . . . . . . . . . 27

Pressure control. 28

Depression of eutectic melting point by a

supercritical fluid in an A-S-SCF system where
A, E are immiscible solids and P1<P2<P3. . . 31
Methods for finding first melting points along
SEV or SSLV phase boundary. . . . . . . . . . 35

Sampling system. . . . . . . . . . . . . . . 38
Sampling positions for the 10-port EPLC valve.39
S-V region beyond the end point of the
C02+naphthalene+phenanthrene SSEV line. . . . 51
Comparison of liquid composition measurements
along SLV line for the C02+naphthalene system.55
Comparison of data from this work and that of Lu

and co-workers. . . . . . . . . . . 56

ix

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

6.1

x
Predicted and measured SDV P-T traces for the

Coz+naphthalene system. . . . . . . . . . . . 7o
Predicted and measured SDV P-T traces for
C02+biphenyl system. . . . . . . . . . . . . 71
Predicted and measured SEV P-T traces

C02+phenanthrene system. . . . . 72

Predicted and measured SLV P-T traces
C02+naphthalene+biphenyl system. . . . . . . 73
Predicted and measured SEV P-T traces
C02+naphthalene+phenanthrene system. . . . . 74
Predicted and measured P-x-y plot along the SLV
line for the C02+naphtha1ene system. . . . . 78
Predicted and measured P-x-y plot along the SLV
line for the C02+biphenyl system. . . . . . . 79
Predicted and measure P-x-y plot along the SLV
line for the C02+phenanthrene system. . . . . 80
Comparison of equation of state phase
equilibrium predictions to experimental data. 81
Comparison of fits of the SEV P-T trace for
different values of kij in the Peng-Robinson
equation for the C02+naphtha1ene system. . 14o

Comparison of fits to the P-x-y plot along the

SBV line for the C02+naphthalene system. . 141
Comparison of fits of the SEV P-T trace for
different values of kij in the Peng-Robinson

142

equation for the C02+biphenyl system. . . .

Figure 3.4

Figure 6.5

Figure 6.6

xi
Comparison of fits to the P-x-y plot along the
SEV line for the C02+biphenyl system. . . . 143
Comparison of fits of the SEV P-T trace for
different values of kij in the Pang-Robinson
equation for the C02+phenanthrene system. . 144
Comparison of fits to the P-x-y plot along the

SEV line for the C02+phenanthrene system. . 145

CHAPTER 1

INTRODUCTION

A supercritical fluid is defined as a component or
mixture of components above its critical temperature and
pressure. The first experiments demonstrating the ability
of a supercritical fluid (SCF) to act as a solvent were
reported over a century ago by Hannay and Hogarth (1879).
For some time this observation remained little more than a
scientific curiosity, but in the last twenty years,
supercritical fluids and their unusual solvent properties
(such as strongly pressure dependent solvating power) have
been applied to an ever widening spectrum of processes.
Most current uses are in the petroleum industry for such
processes as deasphalting heavy crude oils and enhanced oil
recovery and the food processing industries for
decaffeination of coffee and extraction of flavors and
aromas. Some applications in the areas of chemical and
polymer processing and waste treatment are now in research
and development. Supercritical fluid chromatography (SFC)
has also emerged as a valuable analytical tool. Full
development of these processes, however, will require a more
thorough understanding of the thermodynamics of high
pressure systems involving supercritical fluids.

In general, the better a process is understood, the
more fully and effectively it is utilized. Distillation,

for example, has been studied and employed for centuries as

1

2
a separations method. It is now arguably a very well
characterized operation. Engineers continue to improve the
technology of distillation, but most improvements are now
relatively incremental.

Less well understood but potentially valuable
technologies, such as supercritical fluid phase operations,
remain underutilized. Full exploitation of the potential of
these emerging processes will require the acquisition of
additional fundamental data, and the development and testing
of models to accurately interpret these data and represent
the underlying thermodynamics.

One notable area in which knowledge is still deficient
is the thermodynamics of multi-phase systems involving
solids and supercritical fluids. (In this dissertation, the
term "solid" refers to compounds which are solid at
atmospheric pressure and room temperature.) As noted by
McHugh and Krukonis (1976):

"... high pressure phase-behavior can be complex

even for simple binary mixtures in which the

components are chemically similar but have

different molecular sizes ... "

In supercritical fluids, the molecules are likely to be
packed nearly as densely as in a liquid. Interactions based
on molecular shape, size, polarity, polarizability, or even
relative orientation can have a profound effect on the phase
behavior of such systems.

To test predictive models for multi-component systems,

the loci of the phase boundaries must be known. Such data

3
for systems involving solids in contact with supercritical
fluids are still relatively scarce.

The goals of this work were: 1) to construct an
apparatus capable of providing phase equilibria data for
solid/SCF systems, 2) to expand the existing data base with
new measurements on both previously studied systems and new
systems for which little or no data existed, and 3) to test
a modification of the Peng-Robinson equation of state to
determine whether improving the volume predictions for the
pure components could also improve the phase equilibrium
predictions for mixtures of these components.

The system assembled for this work consisted of a view
cell to permit visual observation of the phase behavior, a
mechanism for sampling fluid phases within the cell, and the
necessary equipment to control the pressure and temperature
in the cell. This apparatus proved suitable for obtaining
the desired phase equilibria data. Several recommendations
will be made at the conclusion of this dissertation,
however, which would improve its capabilities.

In this work, P-T-V-x-y data for the C02+naphthalene
system and P-T data for the C02+phenanthrene system were
measured along the SLV lines. P-T data were obtained along
the SSLV lines for the C02+naphthalene+1 ternary systems
where the third components 1 a biphenyl, phenanthrene,
acenaphthene, or anthracene. Four sets of P-T-V-x-y data
were also obtained in the three phase regions of the

C02+naphthalene+biphenyl ternary system. These systems were

4

chosen for reasons of safety, availability, and the
likelihood that they would form the type of systems of
interest for this work. The systems did form the desired
type of binary systems, but the phase behavior of some of
the ternary systems was a little different than expected.

The results of the modeling of the systems in this work
indicate that improving the predictions of the pure
component volumes by volume translations can improve the
equilibrium phase predictions for those components in
mixtures. The improvement is most conspicuous when the
translations are largest.

The remaining chapters in this dissertation discuss in
more detail the phase behavior being studied, the methods
and models used to study them in this work, and how this

work relates to corresponding work done elsewhere.

CHAPTER 2

BACXGROUND ON MULTI-PHASE EQUILIBRIUM

To put the work reported in this dissertation in
perspective and clarify some of the terms necessary to
describe the observed behavior, a short discussion of phase
diagrams is presented. To simplify this discussion, the
phase diagrams for mixtures of a single SCF with a single
solute. will be used to provide a basis for understanding
and explaining the phase behavior of multi—component
SCF-solute mixtures.

Phase Diagrams for Supercritical Fluid-Solute Mixtures

According to the Gibbs phase rule, the degrees of
freedom in any non-reacting system may be determined by the

relation:

F=2+C-P (2-1)

Where F is the degrees of freedom (number of independent
intensive variables), C is the number of components, and P
is the number of phases. In a binary system, this means
that when three phases are in equilibrium, such as a solid,
a liquid and a vapor, specifying a single intensive variable
will fix the values of all other intensive variables.
Alternatively, if a critical phase is present, two of the
degrees of freedom are used by equations which define a

critical condition. Where four phases are in equilibrium or

6
a single phase is in equilibrium with a critical phase, all
variables are fixed, resulting in an "invariant point".
These lines and points are shown in Figure 2.1 as
projections on pressure-temperature (P-T) diagrams to
illustrate the types of phase behavior which may be
encountered. The letter classification scheme shown in this
figure is that given by Luke (1986) and will be used in this
dissertation when referring to the different classes of
binary phase behavior.

Mixtures where the two components have very similar
triple points and critical points tend to form type A
systems. As molecular disparities increase, the triple
points and critical points become more dissimilar and
regions of liquid-liquid-vapor (LLV) immiscibility appear.
When two components are sufficiently dissimilar, the binary
mixture will form a type F system with two distinct branches
separated in temperature by a solid-vapor region. This type
of behavior is typical of systems where one component is a
light gas such as ethane, ethylene, or CO2 (which are
commonly used SCF's) and the other component is a heavy
compound which is normally solid at room temperature.

Figure 2.2 illustrates a portion of the type F P-T
diagram in more detail. The light component (or SCF) is
denoted by the subscript "a". Component "b" is the heavy
component. Ca and Cb indicate the critical points of the
respective pure components. The triple point of the pure

solid is designated by the triangle. On the lower

--.‘a.o

 

 

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h
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v!
v:
a:
L.
O.
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Figure 2.1 Six types of binary fluid phase behavior. T1

and T2 - components 1 and 2 triple points, C1
and C2 - component 1 and 2 critical points,
81 an 82 - S LV (solid component 1 + liquid
+ vapor) 2and 2L‘V equilibrium lines, III -
LLV equilibrium, K - critical end point, Q -
quadruple point, CST - critical solution
terminal point.

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9
temperature branch, the solid-liquid-vapor (SLV) line
intersects the critical mixture curve at the lower critical
end point (LCEP), which is denoted in Figure 2.2 as C1. The
SLV line of such a system often lies very close to the VLE
curve of the light component, and is very difficult to
distinguish on a P-T plot of experimental data. The SLN
line of the upper branch intersects the critical mixture
curve at the upper critical end point (UCEP), which is
denoted in Figure 2.2 as C2. This was the branch studied
for the binary systems in this work. It may be noted that
as more of the lighter component dissolves into the liquid
with increasing pressure along this line, the melting point
of the solid is initially depressed. For many systems, the
slope of the upper branch SLV line on the P-T diagram
remains negative until it intersects the critical mixture
curve. However, for other binary systems of organic solids
with C02, including those studied in this work, the SLN line
reaches a minimum in temperature and then begins to curve

gradually back up in temperature until it reaches the UCEP.

Phase behavior in ternary systems is more complex, but
analogous to that in binary systems. According to the Gibbs
phase rule (eqn. 2.1), four phases may co-exist along a line
on the P-T diagram. Invariant points occur where either
five phases or one critical phase and two additional phases
are in equilibrium. In work with a ternary mixture of

ethylene, naphthalene, and hexachloroethane, van Gunst et

10
al. (van Gunst 1953b) observed a temperature depression of
the SSLV ternary eutectic line. As shown in Figure 2.3,
such systems may exhibit two ternary critical end points,
designated as the "p” (lower temperature) and "q" (higher
temperature) points. Ternary systems may display such an
interruption of the critical locus if the binary mixtures of
the individual solids with the solvent gas also have
interrupted critical loci. The existence of the LCEP and
UCEP for each of the SCF-solid binaries does not, however,
mandate such an interruption of the ternary critical locus,
i.e. type F behavior by the binaries does not always lead to
type F analogue behavior for the ternary. Most of the
measurements done on ternary systems in this work were
carried out along the upper branch SSLV line beginning at
the binary eutectic of two solids.

It can also be helpful to plot the compositions of the
phases in equilibrium along the binary system SLN and
ternary system SSLN lines. When a system has a critical end
point the compositions of the liquid and vapor phases will
meet at the critical end point. For the binary systems, all
component compositions are fully represented by a single
plot on a pressure vs. composition (P-x-y) diagram.

In a ternary system, a ternary or triangular diagram is
needed to represent the mole fractions of all components
simultaneously. Compositions may be plotted along the SSLV

line, SBV isotherms, or SLV isobars. At fixed pressure and

11

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12
temperature, phase compositions and tie lines may also be
plotted on a ternary diagram.

Figure 2.4 illustrates this type of diagram for a
ternary system at a pressure and temperature between the
first meltingand first freezing points for the two solids.
This corresponds to a region in Figure 2.3 between the
SbScLV line and the SbLV and SCLV lines. Figure 2.4 shows
the different types of phase behavior which would be
observed at different overall compositions. In some
composition regions, a single phase of variable composition
will exist. For example, at high SCF solvent mole
fractions, only one vapor phase will exist. In regions
where two phases may coexist, tie lines specify the
compositions of the equilibrium phases. The diagram also
has regions where three phases will coexist at fixed
compositions but in variable quantities. The circles and
triangles on the diagram indicate the compositions of the
vapor and liquid phases respectively at SLV conditions.
Changes in pressure or temperature change the appearance of
the diagram in a systematic manner. As the SSLV line is
approached, the region between the circles and the triangles
becomes compressed until the left and right sides merge to
form a line with one circle and one triangle (which
represent the equilibrium vapor and liquid compositions).
As the ternary UCEP is approached, the region collapses to a

single point.

13

8 CF

 

 

Solid c

Figure 2.4 Ternary composition diagram at fixed pressure
and temperature. S - solid, L - liquid, V -
vapor, subscripts b and c refer to the two
solids.

14

In order to put the research reported here in
perspective, the remainder of this chapter is devoted to
discussing the related work of other researchers.
Historical Perspective

Researchers have compiled considerable data on
solubilities and phase behavior in many systems involving
supercritical fluids. Much of the available information has
been reviewed by McHugh and Krukonis (1986). Additionally,
the two authors compiled a list of most of the reviews on
the topic published up through 1985 (Paulaitis et al.
1983a, Randall 1982, Johnston 1984, Brunner and Peter 1981,
Williams 1981, Irani and Funk 1977, Paul and Wise 1971,
Valertis 1966) and symposium proceedings (Kénigstein 1984,
England 1983, Paulaitis et al. 1983b, Schneider et al. 1980,
Penninger et al. 1985, Charpentier and Sevenants 1987,
Johnston and Penninger 1989). Since many excellent review
papers and books have already been published on the subject,
completely duplicating their information for this
dissertation would be superfluous. The focus of this
research was on phase equilibria of organic solids with
carbon dioxide, so only previous work directly related to
that topic is noted here.
Experimental Studies of Solid-SCF Systems

The first report of the ability of supercritical fluids
to dissolve solids came in 1879 at a meeting of the Royal
Society of London. Hannay and Hogarth presented the results

of experiments in which they observed that changes in

15
pressure caused several inorganic salts to dissolve into or
precipitate from supercritical ethanol (Hannay and Hogarth,
1879 and 1880). In 1896, Villard, published a review of
supercritical fluid solubility phenomena including a
description of the depression of the melting point of pure
solid camphor contacted with ethylene at elevated pressures
(Villard, 1896). E. H. Bfichner also reviewed the literature
in 1906, adding his own data and observations of SCF-solute
systems. He reported cloud points, freezing points, and
number of phases in his solubility studies (Bfichner, 1906).
Not long thereafter Prins studied phase behavior of
naphthalene with supercritical carbon dioxide and ethylene
(Prins, 1915). His experiments included determination of
three-phase border curves and critical end points for
naphthalene in both gases.

Most additional work on phase behavior of solids in
supercritical fluids until the late 1940's was concerned
with inorganic solutes and fluids such as water. In 1948
Diepen and Scheffer published a study of phase behavior of
binary systems involving organic solids and supercritical
ethylene (Diepen & Scheffer, 1948). In their article, they
reported P-T (pressure-temperature) data along phase
boundaries and critical loci for eleven systems. Nine of
the systems were type F. This is the class of binary
systems into which the binary systems studied in this work
fall. The P-T traces of the SLV lines in those nine systems

exhibit melting point depressions of the solids. Two papers

16
by van Gunst, Scheffer and Diepen (l953a,b) presented
additional P-T phase boundary data for seven binary systems
of ethylene and organic solids and one ternary system of
ethylene with naphthalene and hexachloroethane. A series of
papers by van Welie and Diepen in 1961 detailed the SLV
boundary for the ethylene+naphthalene system including
pressure, temperature, volume and phase compositions along
the SLV line up to the upper critical endpoint of the line
(van Welie and Diepen 1961a-e).

Additional studies by several individuals and groups
have explored type F phase behavior of mixtures of solids
with supercritical fluids. Table 2.1 lists researchers and
systems studied. Studies involving ternary systems where
the supercritical fluid forms a type F system as a binary
with one of the two solutes are listed in Table 2.2. At the
time the work reported in this dissertation was initiated,
little phase behavior data other than solubilities of solids
in supercritical fluids existed for ternary systems where
both heavy components formed type F systems with the light
component. (Van Gunst et al. (1953b) gave P-T trace data
but no composition data along SSLV lines were available.)

All the studies listed in Tables 2.1 and 2.2 include
SLV or SSLV P-T trace data or solid solubilities in the
supercritical fluid. A limited number include composition
measurements along the SLV lines in binary systems. Cheong
(1986), Zhang (1988), and Lu (1989) report upper branch P-T

trace data and liquid compositions along the upper branch

17

Table 2.1

Previously Investigated Type F SCF + Solid Systems

Smits (1903-04a,b:
1904-05: l905-06a,b:
1909-10)

Smits and Treub
(1911-12&,b)

Verchoyle (1931)

Diepen and Scheffer
(1948)

van Gunst et al. (1953a)

van Welie et al.
(1961a-e)

Diepen and van Hest
(1963)

Rodrigues and Kohn (1967)
Streett and Hill (1971)

Streett and Erickson
(1972)

Kuebler and McKinley
(1976)

(CH CH2) 0 +
Antgraqu none

(CH CH2)20 +
Ant raqu1none

Hz + co
CH =CH +
1 3,5- richlorobenzene

p-Chloroiodobenzne
p-Dibromobenzene
Octacosane
Hexatriacontane
Naphthalene
Biphenyl
Benzophenone

CH =CH2 +

An hracene
Hexaethylbenzene
Hexamethylbenzene
Stilbene
m-Dinitrotoluene
Naphthalene

CHZ-CHz + Naphthalene
CH4 + Naphthalene

Ethane + Octacosane
Ne + Ar
He + Ar

CH4 + Benzene
CH4 + Toluene

18

Table 2.1
(cont.)

Kohn et al. (1977)

Tiffin et al. (1979a)

Kohn et al. (1980)

Tsang et al. (1980)
Tsang and Streett (1981a)
Tsang and Streett (1981b)

McHugh (1981)

McHugh et al. (1984)

McHugh and Yogan (1984)

Krukonis et al. (1984)

Cheong et a1. (1986)

McHugh et al. (1988)
Zhang et al. (1988)

Lemert and Johnston
(1989)

Lu and Zhang (1989)

Yamamoto et al. (1989)

CH4 + Octane
CH4 + Cyclohexane

Ethane + Naphthalene

CH2=CH + n-Eicosane
CH2=CH2 + n-dotriacontane

H2 + CH4
H2 + C02
H2 + C0

C02 + Naphthalene
C02 + Biphenyl

CO2 + Octacosane

Ethane + Biphenyl
Ethane + Ocatacosane
CH2=CH2 + Biphenyl
CH2=CH + Octacosane
C02 + Naphthalene
C02 + Biphenyl

C02 + Octacosane

Xe + Naphthalene

C02 + Naphthalene
C02 + Biphenyl

Xe + Naphthalene
C02 + Phenanthrene

002 + Naphthalene
C02 + 2-Naphthol

C02 + Naphthalene
C02 + m-Terphenyl

CD2 + Indole
C02 + Quinoxaline

19
Table 2.2

Ternary Systems

Verchoyle (1931) H2 + C0 + N2

van Gunst (1950) CH2=CH + Naphthalene +
Hexach oroethane

van Gunst et al. CH2=CH + Naphthalene +

(1953b) Hexach oroethane

Tiffin et al. CH4 + Ethane + Benzene

(1979b) CH4 + Ethane + Cyclohexane

Zhang et al. (1988) C02 + Naphthalene + Biphenyl
CO2 + Naphthalene + Phenanthrene

Lemert and Johnston CD2 + n-Pentane + Naphthalene

(1989) CD2 + Methanol + 2-Naphthol

 

for the binaries they studied. Lu and Zhang (1989) also
determined P-T-x values at three temperatures along the
critical locus near the UCEP (upper critical end point) for
the C02+naphthalene system. Using these data, they
determined the pressure, temperature and composition at the
UCEP. Yamamoto et al. (1989) measured vapor phase
composition along the three phase lines in their study.
Zhang et al. (1988) report liquid phase compositions along
what they believed was the four phase line (SSLV) for the
two ternary systems they studied. However, their method
used a first freezing method, which actually provided only
three phase equilibrium.
View Cells

A view cell in which phase changes can be observed is

requisite for any study of melting points. To contain the

20
pressures in supercritical fluid studies, these view cells
generally fall into two categories: thick walled glass tubes
and metal cells with windows. Each type has inherent
advantages and drawbacks.

The apparatus used by Hannay and Hogarth (1879)
consisted of a thick walled, small i.d. glass tube attached
to a pressure generating device. Van Welie (1961a), Luks et
a1. (Fall and Luks 1984, Jangkamolkulchai et al. 1988),
McHugh (1981), and Lemert (1989) also used thick walled
glass tubes in their phase equlibria studies. These view
cells are relatively inexpensive to construct and have no
blind spots in viewing. 0n the other hand they are limited
in the pressures they can contain and tend to fail
unpredictably.

Kohn (1956), Lu et al. (Cheong et al. 1986, Zhang et
al., Lu and Zhang 1989) and Yamamoto et al. (1989) used high
pressure liquid level sight gauges in their investigations.
Custom made steel optical cells are also commonly used by
researchers. (Lentz 1969, Brennecke and Eckert 1989,
Johnston et al. 1989, Smith et al. 1989, Beckman et al.
1989) A custom built optical cell was used for the work
reported in this dissertation. Such cells can be
constructed to hold very high pressures. The high thermal
inertia of the metal (usually steel) walls can also be an
advantage in maintaining an isothermal environment for the
enclosed system. Flat windows in windowed cells aide

studies using ultraviolet spectrophotometry or other

21
non-invasive analytical techniques where uniform optical
pathways may be advantageous. These cells are, however,
usually much more expensive to construct than the glass tube
type. The metal walls may also obscure portions of the
cell, thus creating blind spots which cannot be monitored.
Composition Determinations

Phase compositions in high pressure systems have been
determined by three different methods: 1) flow system
sampling, 2) quasi-static sampling, and 3) synthetic
methods. Each method has inherent limitations.

Sampling near a solid/fluid phase boundary tends to be
very difficult due to the potential for solidification of
some components in the sampling lines. The problem is worst
for liquid phases, which are much richer in the components
which solidify. There is also the likelihood of depleting
the solid solutes during sampling. Synthetic methods
usually require custom made cells (which are expensive) and
can easily leak if not machined with sufficient precision.
Since these methods rely on accurate determination of the
amount of each component charged to the cell before the
experiment begins, any leakage introduces error by allowing
unknown quantities of the components to escape.

Direct sampling can be done either in a flow system, or
by a quasi-static method. Although several different flow
methods are described in the literature,(Prausnitz and
Benson 1959, Simnick et al. 1977, Van Leer and Paulaitis

1980, Johnston and Eckert 1981, Kurnik et al. 1981, Schmitt

22

1984, Krukonis & Kurnik 1985), they all embody the same
basic features. In a typical flow system, a solid sample is
first placed in the system, the system is flushed and
pressurized with the solvent gas, and the system is then
brought to equilibrium. Once equilibrium has been
established, a sampling valve is Opened and a continuous
supply of the solvent gas is pumped through the system,
becoming saturated with solutes as it passes through. This
method is usually limited to sampling the vapor phase. If a
liquid phase is also present, care must be exercised to
prevent entrainment of the liquid in the vapor which would
produce errors in the composition determination.

Quasi-static sampling methods involve taking small
samples from an otherwise closed system. The research group
of Dr. C. -Y. Lu (Cheong et al. 1986, Zhang et al. 1988)
constructed an apparatus which samples the liquid phase
using a three way valve which is evacuated and then turned
to connect it with the view cell. The pressure in the cell
pushes the liquid into the evacuated valve. The sample thus
obtained is expanded to atmospheric pressure and the
composition analyzed. Legret et al. (1981) constructed a
high pressure sampling micro-cell which could be used to
take a sample directly from the vapor phase and inject it,
still under pressure, into a gas chromatograph for analysis.
In this work, a method was developed for sampling both

phases. Details of the method are contained in Chapter 4.

23

For a synthetic method, phase compositions are
determined by introducing known amounts of the components
into the cell and adjusting the pressure or temperature
until phase transitions occur. Van Welie and Diepen (1961
a-e) used this method in their studies of the
ethylene+naphthalene system. By doing multiple
determinations over a range of temperatures or pressures for
each fluid (liquid or vapor) phase, and extrapolating the
constant composition lines on a P-T diagram to their
intersection with the previously determined P-T trace of the
three phase (SLV) line, they determined the equilibrium
phase compositions along the SLV phase boundary. A similar
technique has also been used by McHugh et al. (1984) to
measure solid solubilities in supercritical fluids. Their
apparatus included a piston which allowed variation of the
total cell volume in addition to the system temperature and
pressure.

With the necessary explanation of the phase behavior to
be studied provided and the relevant work of other
researchers discussed in this chapter, the work done for

this dissertation can now be presented.

CHAPTER 3

EXPERIMENTAL APPARATUS

The experimental apparatus allows for control of the
pressure and temperature within the experimental cell,
observation of the phase of the cell contents, and sampling of
the contents of the cell.

View Cell

Figure 3.1 shows a cross section of the view cell. This
cell is fabricated from 316 stainless steel. The interior of
the cell is illuminated through the window at the top of the
cell by a fiberoptic light. The state of the contents is
observed through the side window by means of a closed circuit
color camera connected to a borescope. The internal volume of
the cell is about 30 cm3. Although view of the upper region
of the cell is restricted, any additional phase formed in this
region must have a mass density less than the mass density of
the supercritical phase. Such behavior is not anticipated
with the systems studied here. The windows are 3/4 inch x 3/4
inch quartz. A triangular magnetic stir bar at the bottom of
the cell stirs the lower phase in the cell. A rectangle of
stainless steel wire mesh on.a shaft epoxied into the magnetic
stir’ bar* stirs the upper* phase. During' melting' point
determination experiments, the solid sample rests on a
stainless steel wire mesh platform at the level of the side
window of the view cell. During sampling experiments, the

platform is replaced with.a narrow stainless steel mesh cross

24

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l V
"A“

 

\
\

 

 

 

 

\.
m

 

 

 

 

 

 

 

 

 

 

Figure 3.1 Cross-sectional diagram of the view cell.
Components are labeled as follows: a - quartz
windows, b - magnetic stir bar, c - wire mesh
flapper, d - sample platform, e - sampling
ports.

26

piece which keeps the vertical shaft axially centered in the
cell during stirring. Two ports through the wall of the cell
opposite the side window permit samples of each phase to be
withdrawn for analysis of composition.
Temperature Control

A schematic is given in Figure 3.2 of the portions of the
apparatus used to control the temperature in the view cell.
The cell is immersed in a water bath. Temperature control
components consist of 1/4" nominal diameter copper cooling
coils (c) (supplied with cold tap water), a 300 watt copper
clad Ni-Cr resistance heater (base heater) (d) controlled with
a.type 3PN1010 Staco‘Energy Products Co. variable transformer,
and a Bayley Instrument Co. Precision Temperature Controller
(model 123) (e) connected to a 500 watt quartz heater. The
temperature within the bath is measured with ASTM thermometers
which were checked against NBS traceable thermometers and
verified to be accurate to 10.05 'C. The temperature within
the cell is measured with a calibrated thermistor (Omega
Engineering, model THX-400-GP) which passes through a
compression fitting into the cell. The water in the bath is
stirred with a T-Line model 105 stirring motor (with a shaft
and propeller) attached to a T-Line model 115 Adjusta-Speed
controller (both from Talboys Engineering Corp.). The motor
was usually run at full speed, i.e. 1550 rpm.
Pressure Control

Figure 3.3 shows the portions of the apparatus used for

control of the pressure. Carbon Dioxide (Linde bone dry

Figure 3.2

 

27

 

 

 

 

 

 

 

 

 

 

Constant temperature bath. Components are
labeled as follows: a - controller temperature
probe, b — quartz makeup heater, c - cooling
coils, d - base heater (connected to variable
voltage transformer), e - temperature
controller, f - thermistor, g - view cell.

28

 

 

 

 

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29
grade) from a supply cylinder (a) is supplied to an air driven
gas compressor (Haskel model AG-152) (b). The pressurized CO2
is fed to a High Pressure Equipment Company model 0C-11
reactor (c) which serves as a reservoir or'ballastm ‘Valves v1
and v2 allow isolation of the reservoir. A Heise model CMM
63457 pressure gauge (f) is used to determine the system
pressure. Valves v4 and v6 allow isolation of the view cell
(9). Safety relief heads (d and e) are installed at the
indicated points to prevent accidental overpressurization of
the system. System pressure is raised by carefully cracking
open valve v2. System pressure is lowered by opening valve v6
and adjusting valve v7, an HIP model 60-HF11-MTS metering
valve, to bleed off'gas at a controlled rate. .Ashcroft 10,000
psi pressure gauges (p1 and p2) are used to monitor pressures
in the reservoir and in the sample loop pressurizing branch.
The four lines extend from a high-pressure cross (h) comprise
the sample loop pressurizing branch. Clockwise from the top,
these lines connect to: 1) a pressure gauge, 2) an open line
which can be connected to the sampling line, 3) a venting
valve, and 4) valve v3. The function of this branch is
explained in the next chapter as part of the sampling

procedure.

CHAPTER 4

EXPERIMENTAL PROCEDURE

Two types of experiments composed the experimental
portion of this work. The first experiments were designed to
determine the P-T traces of the melting point curves in binary
and ternary systems. The C02+phenanthrene, C02+naphthalene,
C02+naphthalene+biphenyl, C02+naphthalene+phenanthrene,
C02+naphthalene+anthracene, and C02+naphthalene+acenaphthene
systems were studied in these experiments. None of the solids
used in this work form solid solutions with naphthalene so all
solid phases are pure. The second set of experiments was
designed to determine the phase compositions along the phase
boundaries. The systems examined in these experiments were
C02+naphthalene and C02+naphthalene+biphenyl.

Melting Point Curve Determination

According to the Gibbs phase rule, binary systems with
three phases (SLV) and ternary systems with four phases (SSLV)
have one degree of freedom. This may be chosen to be the
system pressure or temperature. Both first melting and
first freezing methods have been used to study melting point
depressions. Both may be used in binary systems, but only the
first.melting method is suitable for studying the SSLN’line in
ternary systems. Figure 4.1 is useful to illustrate this.
The figure is drawn on a solvent free basis and represents the
shift in the pure solid melting points and mixture eutectic

with changes in pressure. For a single solid the first

30

31

 

 

 

 

 

 

 

P1
P2
93
:3 P3
...-I
as
I...
a)
D.
E
a)
l- ,
T1
T2 K ‘3?/
T3 H
O 1
Mole Fraction Component A
-. (on a supercritical fluid free basis)
Figure 4.1 Depression of eutectic melting point by a

supercritical fluid in an A—B-SCF system,
where A, B are immiscible solids and P <P <P .
The upper lines represent first freezing and
the lower lines represent first melting. T1
is the eutectic temperature at pressure P1

32
freezing point will be identical to the first melting point,
although changing the pressure will shift this point. First
melting and first freezing experiments correspond to
approaching this melting/freezing point from above and below
respectively. In contrast, in a mixture of solids melting and
freezing will occur over a range of temperatures at fixed
pressure. Consider the equilibrium line at pressure P1 with
eutectic temperature T1. For a composition between a pure
component and the eutectic composition, if melting is
approached from below (the solid side), the first melting will
occur at the eutectic temperature T1 and the first liquid will
be at the eutectic composition. Above this temperature, no
more than one of the components in the binary system may
remain solid. Increasing the temperature will continue to
melt the remaining solid phase (changing the liquid
composition) until the equilibrium curve is reached. The
temperature at which the last solid melts corresponds to the
first freezing point for the liquid at that composition.
Unless the solid/solid ratio is precisely that of the
eutectic, using a first freezing method in a ternary system
would yield points on a three phase surface, not along the
SSLV line. From the Gibbs phase rule, a ternary system with
three phases will have two degrees of freedom so fixing either
the pressure or the temperature alone will not uniquely
determine all other variables of the system, hence a surface

is defined rather than a line.

33

In this work, sample preparation is similar for both the
binary and the ternary systems. For binary system
measurements, some of the solid is melted and drawn into a
section of capillary tubing of 2 mm i.d. or smaller using a
small pipet bulb. The upper (non-sample) end of the tube is
quickly sealed with a fingertip to prevent the liquid sample
from draining out and the tube is removed from the liquid
container and allowed to solidify: IA 3/4 inch section of this
filled tubing is placed on the wire platform and serves to
hold the portion of the sample being studied in a constant
position and prevent it from draining away completely when
melting occurs.

For ternary measurements of the SSLV line, the two solids
to be used in the study are first mixed to provide intimate
contact. The minimum melting point for the solid-solid binary
at atmospheric conditions occurs at the eutectic composition.
A solid mixture of this composition is prepared in the
expectation that a similar ratio of the components will be
present in the liquid phase at the first melting point in the
ternary mixture. The solid mixture is melted in a test tube
and stirred to obtain a homogenous liquid. Some of the liquid
is drawn into a capillary tube. The remaining liquid is
poured out onto a clean sheet of aluminum foil. After the
binary liquid cools and solidifies, the thin sheet of solid
material is broken up into "flakes" for loading into the view

cell.

34

Once the sample is prepared, adequate solid (1 to 2
grams) is loaded into the view cell to ensure the presence of
excess solid at all conditions to be studied. The capillary
tube is placed on the wire mesh platform as close as possible
to the side window and parallel to it. With the sample
loaded, the cell is sealed, placed in the temperature control
bath, and connected to the high pressure gas reservoir. The
cell is purged with the solvent gas and then pressurized with
enough of the solvent fluid to bring it near the desired final
pressure. The bath is also heated or cooled to near the
desired temperature. The contents of the cell are stirred at
least 20 minutes to ensure that thermal and composition
equilibrium have been achieved before initiating measurements.
Thermal equilibration was confirmed using the thermistor
installed in the cell wall.

Measurements are made by two methods. Method A (see
Figure 4.2) is used in the initial lower pressure region where
the decrease in melting point with increasing pressure is most
rapid. The temperature of the bath is held constant and the
pressure in the cell is varied by adding and releasing small
amounts of the vapor phase. The pressure at which the first
melting occurred within the capillary tube (near the ends) is
recorded as the melting point. Accuracies for these
measurements are i 0.35 bar and i 0.05 K.

In the higher pressure region where the P-T curve becomes
almost parallel to the pressure axis, method B (Figure 4.2) is

used. The pressure of the cell is raised to near the desired

35

    

 

2
:3
U)
8
L.
D.
Method A
Temperature
Figure 4.2 Methods for finding first melting points

along SLV or SSLV phase boundary.

36

level and then the temperature is raised about 1.0 K/hour
until the first melting is observed” .At this rate of heating,
thermal lag between the bath temperature and the temperature
within the cell was less than 0.1 K. For this method, both
the pressure and the temperature are changing with time.
Accuracies for these measurements are i 0.1 bar and i 0.2 K.
Method B corresponds to the method used by McHugh (1981) to
determine similar P-T traces.
Sampling

One of the important parameters in phase equilibrium of
multi-component systems is the composition of the phases. For
this reason the view cell was designed to allow sampling of
fluid.phases (liquid, gas, or supercritical fluid). The first
step in obtaining equilibrium composition data is to bring the
system to the desired equilibrium state. For the binary
systems, the pressure was fixed and the temperature was raised
high enough to melt all solid. The temperature was adjusted
until the first solid began to precipitate. For the ternary
system, the temperature was the fixed variable while the
pressure was gradually lowered until solid began
precipitating. Pressures and temperatures were chosen to
minimize the amount of solids in the cell, and thus avoid
plugging the sampling ports, the HPLC valve and the lines
leading to the HPLC valve and the plug valves. ,All samples in
this work.were taken along three phase boundaries (SLV). For
the ternary system, this means data points are on a three

phase surface instead of along a four phase linen To maximize

37

the information from these experiments, the cell was loaded
with various initial naphthalene/biphenyl ratios different
from the eutectic ratio and the sampling repeated at the same
temperatures for each initial ratio. These isotherms should
allow the phase boundary surfaces of this system to be at
least partially defined by the intersection of the isotherms.

Figure 4.3 is a schematic of the equipment used for
sampling; IAs shown in Figure 3.1, the view cell has two ports
through which samples of the cell contents may be drawn.
These two ports are connected to two ports of a Valco model
C10W 10-port HPLC sampling valve (from Valco Instrument Co.
Inc.) (e). The other HPLC valve ports connect to two sample
loops, two plug valves (f1 and f2) and a flush line. Valves
f1 and f2 are Whitey SS-4PDF4 rising plug valves with one end
sealed on each with a stainless steel pipe plug. This allows
the valves to be used as high pressure syringes with
approximately 1 cc capacity. Figure 4.4 shows the two
positions of the sampling valve. In position 1, the sample
line is connected to the vapor sample loop while the liquid
sample loop is in line with the cell and plug valve f2. In
this position, the vapor sample loop is flushed when the
sample line is flushed. In position 1, it is also possible to
draw a sample into the liquid sample loop with plug valve f2.
In position 2, the sample line is connected to the liquid
sample line while the vapor sample loop is in line with the
cell and plug valve f1. In this position, the liquid sample

loop is flushed when the sample line is flushed. In position

38

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n.v ensues

39

to plug to upper port
val of cell

   
   

Posifion 1

samph sampm
line line

   
 

In plug in lower
valve port of cell

to plug to upper port
valve of cell

Posilion 2

   

sample sample
line line
to plug to lower
valve port ol cell
Figure 4.4 Sampling positions for the lo-port HPLC valve.

Position 1 allows sampling of the vapor phase.
Position 2 allows sampling of the liquid
phase.

40
2, it is also possible to draw a sample into the vapor sample
loop with plug valve f1.

Initially, an attempt was made to take a sample with each
switch of valve position, thus sampling the phases
alternately. This proved unfeasible, because when a sample
loop at atmospheric pressure is switched in line with the
cell, the pressure drop from the cell to the sample loop
allows solids to precipitate and block the sample loop or the
line from the cell to the loop before an equilibrium sample
can fill the loop. To avoid this problem, a second method was
devised.

The sample line and sample loop are first flushed with
toluene to remove all residual solutes then dried with flowing
C02 to remove residual toluene. The line and loop are then
pressurized to the same pressure as the cell with CO2 and the
valve is switched to put the sample loop in line with the
cell. Pressurizing the sample loop prevents a pressure
gradient between the loop and the cell and the consequent
premature solid precipitation. The sample line is again
flushed with toluene to remove solutes which enter the line
from the second sample loop (which was connected to the cell
before switching). The sample line and this second loop are
dried with C02 and left at atmospheric pressure. A sample is
drawn into the first sample loop. The sample is drawn slowly
to prevent solid precipitation and to avoid severely
perturbing the equilibrium in the cell and thus getting a non-

equilibrium sample. Some perturbation of the cell is

41

unavoidable during this process because the cell volume is
effectively increased by the volume of the sample taken.
Since the volume of the sample is small relative to the volume
of the cell however, no change in pressure was noticed until
the cell pressure exceeded about 200 bar. Above that
pressure, sampling caused pressure drops of 0.1 to 1.0 bar in
the C02+naphthalene system. This is expected since this
region is near the upper critical end point of the binary
system where molar volumes change rapidly with pressure.

Once the sample is in the loop, the sample valve is
returned to the original position. The sample line is opened
and the volume of<gas released is measured, Since the line is
at atmospheric pressure before this switch, the volume of the
gas released when the sample line is opened is equal to the
volume of gas in the sample loop alone expanded to ambient
conditions. The sample line is then flushed with toluene to
recover the solid portion of the sample. Specifics of the
sampling procedure are outlined in the next section to allow
duplication of the method.
The procedure for sampling the liquid phase is as follows:
1) W

A. The HPLC valve (e) is set to position 1.

B. Valves v8 and v9 are opened.

C. A syringe filled with toluene is connected to the

Knurl-Lok finger tightened HPLC union (g).
D. The sample loop is cleaned. Approximately 30 cc's

of toluene is flushed through the line and sample

2)

42
loop and into a beaker. This volume was chosen
after analyzing samples of the exiting solvent on a
gas chromatograph to find the flush volume which

assured no residual solute could be detected in the

solvent.

E. The beaker is removed to dispose of the waste
solvent.

F. The syringe is removed and the CO2 tank (j)
connected to the Knurl-Lok fitting.

G. The C02 is used to blow the line and loop dry of
toluene and fill them with CO2 at ambient
conditions. Flushing for 30 to 45 seconds proved
sufficient to produce a solvent free stream of gas
from the sample line.

W

A. Valve v8 is closed.

B. The C02 is disconnected and the loop pressurizing
branch (h) is connected to the Knurl-Lok fitting.

C. If valve v4 is open, it is closed. (valve v3 is
already closed at this point.)

D. Valve v5 (see Figure 3.3) is closed to isolate the
cell.

E. The pressure reading on the Heise gauge (f on
Figure 3.3) is noted.

F. Valve v3 is opened.

G. Valve v2 (Figure 3.3) is opened slightly and enough

CO2 is bled in from the reservoir (c - Figure 3.3)

3)

43
to raise the pressure back to that noted in step E.

Once this pressure is reached, valve v2 is closed.

H. Valve v3 is closed (to isolate the sample loop).

I. The HPLC valve is switched to position 2.

J. Plug valve f2 is closed 3 turn.

K. Valve v5 is opened.

W

A. Valve v8 is opened to allow all the pressure in the
line to be relieved. If any pressure remains
(because of precipitated solid blocking the line),
valve v4 is opened to relieve it.

B. A syringe filled with toluene is connected to the
Knurl-Lok union.

C. Approximately 30 cc's of toluene is flushed through
the line and sample loop and into a beaker. If the
line is plugged (because of precipitated solid
blocking the line), the hand pressure generator
(HIP Model 62-6-10) (1) is connected to the Knurl-
Lok union and used to force toluene through the
line to dissolve the solid.

D. The beaker is removed and the waste solvent
disposed of.

E. The syringe is removed and the CO2 tank is
connected to the Knurl-Lok fitting.

F. The CO2 is used to blow the line and loop dry of

toluene and fill them with CO2 at ambient

conditions. (See step 16).

4)

G.

44

Valves v8 and v9 are closed.

:1! . J i . J 2 l

I.

J.

The three-way valve (d) is opened to the
atmosphere, the burette and the flask to keep the
pressure in the flask and the burette ambient when
step 48 is performed.

A 25 ml volumetric flask (c) with 2.5 cc of toluene
containing an internal standard is attached to the
outlet from the sampling line.

The three-way ‘valve is turned to connect the
volumetric flask to the burette (a) only.

The liquid level in the burette is recorded.

The magnetic stirrer is turned off.

To draw a liquid sample, plug valve f2 is slowly
opened 1 turn to draw about 0.25 cc through the
sample loop. (The liquid sample loop internal
volume is approximately 0.05 cc.)

The HPLC valve is turned to position 1.

The magnetic stirrer is turned on

Valve v8 is opened.

The hand pressure generator (i) is connected to the
Knurl-Lok union and turned until some resistance is
felt.

Valve v9 is opened.

The hand pressure generator is turned until the
first drop of toluene can be seen at the tip of the

outlet line entering the flask.

45
The overflow bottle (b) is lowered until the water
level matches that of the burette.
The liquid level in the burette is recorded.
The total gas volume is determined from the
displaced volume of water minus the sample line
volume.
The pressure generator is disconnected and a
syringe filled with toluene is used to flush 22.5
cc of toluene through the line and sample loop to
fill the volumetric flask to 25 cc.
The flask is removed and a small magnetic spin bar
is added before it is capped and placed on a
magnetic stirring plate.
The ambient temperature is read from an ASTM
thermometer (calibrated against an NBS traceable
standard) and recorded.
The ambient pressure is read from a barometer
(Cole-Parmer aneroid barometer stock# N-03316-70)
and recorded.
The line and loop are flushed with another 5 cc of
toluene.
The syringe is removed and the C02 tank is
connected to the Knurl-Lok fitting.
The C02 is used to blow the line and loop dry of
toluene and fill them with CO2 at ambient

conditions.

46

Samples of the vapor phase are taken in the same way as the

liquid with the following exceptions:

1) The HPLC valve is set to position 2 for step #2A.

2) In step #21 the HPLC valve is switched from position 2 to
position 1.

3) In step #2J plug valve fl is closed about 1% turns.

4) A 10 ml volumetric flask with 1 cc of internal standard
solution is used for step #4B.

5) In step #4f valve fl is turned about 1% turns to draw
about 0.3 cc through the sample loop. (The vapor sample
loop volume is approximately 0.05 cc.)

6) In step #4G the HPLC valve is switched from.position l‘to
position 2.

7) It is usually not necessary to use the hand pressure
generator so steps #4J and #4L can be skipped and only
the initial burette liquid level is subtracted to get the
total gas volume in step #40.

8) Only 9 cc of toluene are used to fill the flask with a
total of 10 cc of liquid in step #4P.

Multiple samples were taken from both the liquid and
vapor phases at each P-T point to be analyzed for composition.
The phase sampled was alternated (i.e. two liquid then two
vapor or one liquid then one vapor) to avoid biasing the
result by the order of the sample.

The cell pressure and temperature must be monitored
throughout the sampling to ensure that constant conditions are

maintained. Cell pressure does drop when the sample loop is

47

pressurized.to»cell pressure, because the loop is connected to
the same line supplying the cell. The volume of the supply
line acts as a ballast to minimize the pressure drop, but it
is necessary to add a small amount of CO2 after each sample to
maintain constant conditions. The entire process for taking
one sample requires at least 30 minutes per sample which
proved sufficient to re-establish equilibrium in the well
stirred cell.
Composition Analysis

Phase compositions were determined by finding the number
of moles of each component in each sample and using these
values to determine mole fractions. The moles Of CO2 were
calculated from the ideal gas law using the ambient pressure
and temperature and the change in gas volume in the burette.
Concentrations (and hence moles) of the heavy solutes in the
toluene were measured on a Perkin-Elmer 8500 gas chromatograph
with an FID detector and automatic integrator. Details of the
chromatographic procedure are contained in Appendix A.
Materials

Chemicals used in this study are listed in Table 4.1.
All chemicals were used without further purification. The
purity of the naphthalene, phenanthrene and biphenyl were
verified by measuring the melting point range of each at
atmospheric pressure.

No significant difference in either melting point range

or gas chromatograms was noted between the naphthalene from

48

 

 

 

 

Table 4.1 Purity of Materials
Chemical Supplier Stated Purity
Acenaphthene Aldrich 99 %
Anthracene Aldrich 99.9 %
Biphenyl Aldrich 99 %
Carbon Dioxide Linde Bone dry grade
Naphthalene Aldrich 99+ %
Naphthalene Alfa Products 99.8 %
Phenanthrene ., Aldrich 98+_:

 

 

 

Aldrich and that from Alfa Products, so no distinction was

made in the experiments or the analysis.

CHAPTER 5

EXPERIMENTAL RESULTS

Melting point experiments

Results of the melting point experiments are given in
Table 5.1. The P-T traces of the SLV lines for the
C02+naphthalene and C02+biphenyl systems have.been.previously
measured to their upper critical end points by other
researchers (McHugh and Yogan 1984, Zhang and Lu 1989) so no
attempt was made to redetermine end points of these systems.
The naphthalene-I-CO2 system was measured to validate the
experimental method. Measurements for the carbon
dioxide+naphthalene+phenanthrene system conducted in the
roughly triangular region shown in Figure 5.1 found no melting
point for the system beyond that found at 64.12 bar and 310.55
bar. This is evidence that an invariant point for the SSLV
line lies within this area. In the C02+naphthalene+biphenyl
system, at pressures slightly above the last (i.e. highest
pressure, lowest temperature) melting point, a second phase
was observed running down the walls of the cell before the
solid sample began to melt. This is evidence that the SSLV
equilibrium line of this system does not terminate in a
SS(L-V) equilibrium point. Two possibilities exist which
would be consistent with these experimental observations. The
first possibility is that the SSLV line may bend downwards in
temperature just beyond the last point measured in this study

and continue to a SSSLV point near the triple point of C02.

49

50

 

mm.mm~ mm.mm
mm.bmm ww.cm
mo.wm~ mm.vv
mo.oon Ho.mn
mm.non mm.wN
mm.mon vm.bH
mv.bon m¢.vd

M Hum

eunueuemammlmusmmeum
nOO+Hacmnmwm+wcwamnunmmz

 

 

mm.HHm nv.nh
mw.an Ho.mm
mw.mHn Nm.¢v
mH.an mo.Hm
m¢.omn ¢N.hH
mh.mmn mm.h

m. Hum

wususummaem muzummmm
aOO+ucununmecuo¢+mcuHenunmmz

 

 

mm.Hnn mo.~m
mc.vnn vw.mn
mb.hnn mw.mm
mm.ovn wh.nv
mH.nvn H¢.Nn
mw.mvn mo.om

M Hdm

useueummaua musmmeHMII
INOO+mcmOMNCHC<+eCeHmnunmez

 

 

Om.Nnn om.m¢~

Ob.Nnn oo.NNN

O¢.Nnn om.OHN

mw.Nnn mm.mmfi

mh.Hnn On.0hH

OH.Nnm on.mmH

O¢.Nnm oo.N¢H

mb.mmn mn.m0H m0.Hnn mv.¢ma

mw.mon vo.mm mw.mmn OH.00H om.nnn ON.QNH

mH.bon mm.mm mm.mmm Nn.om om.¢nn vo.NOH
mm.mon NN.bh mw.wmn w¢.vo mm.wnn mv.mm
mm.oan NH.¢@ mo.mmn mm.mb mh.wnn mH.mh
mw.HHn vm.om mm.mmn mm.wh om.ovn ow.mm
mh.mHn ho.wn mm.mmn mm.o> mH.ovn mH.wm
mm.wdn mm.m~ mN.Hwn on.Hm mm.H¢n mm.mm
mH.mHn mm.wH mH.vwn wm.m¢ mn.wvn mo.nn
mm.HNn om.m mw.th no.H mm.hvn wm.mN
Ix Mom In Ham M Hum

unsusuemsemeHSmmeum unsweucmeem eusmmeum mususuemfiemuusmumum

soo+mcmunucecmnm+esmasnunmmz noo+msuunucscmnm ooo+oceasnunacz

eaoamhm soaueoouphm+uoo 0 new pecan apaunuawsvn
same one bum ens omega even ewsueuemseaIeHSueeum deucelwuemum u.n sands

1201

100+

Pressure (bar)
0 O
‘3 L

O
O
a

204

51

..‘.--.C‘

 

 

 

270

Figure 5.1

250 250 300 310 320 330
Temperature (K)

-£F-ILPLefinn
-*—-S-V¢wwfiflmn
-’- C02 v.p. carve

S-V region beyond the end point of the
C02+naphthalene+phenanthrene SSLV line.

52
This would be analogous to a type A or B binary system (see
Figure 1.1). The second possibility is that the SSLN'line may
terminate in a SSLLV point where the first liquid is organic
rich and the second is a C02 rich liquid phase. This would be
analogous to a type C, D or E binary system.

In this work, ternary eutectic melting'point depressions
were determined over a range from the solid-solid eutectic to
near an apparent UCEP for the C02+naphthalene+phenanthrene
system. This critical endpoint seems to occur hundreds of bar
below the'UCEP's for the C02+naphthalene and C02+phenanthrene
systems. The C02+naphthalene+biphenyl melting point
depression line was measured to near the C02 vapor pressure
curve where more complicated phase behavior interfered with
measurement.

Composition measurements

Compositions of the vapor and liquid phases were measured
for the C02+naphthalene system along the three phase (SLV)
line and for the C02+naphthalene+biphenyl system along three
phase (SLV) isotherms. Results are given in Tables 5.2 and
5.3. For these measurements, mixtures of naphthalene and
biphenyl at several overall compositions different from the
expected eutectic compositions were prepared and loaded into
the cell. Sampling for both the binary and ternary systems
was carried out as described in Chapter 4. The raw data are
tabulated in Appendix H. Average values were taken as the
correct values with the values of obviously poor samples

excluded.

53

.emch peeved pcoowu c sown aanenoum one came omens ««

 

 

 

..664¢.~m omme.om ..mnnoo.o .«mosoo.o mo~.o ~m~.o oo.mon m.¢s

ommn.me~ «was.sos mmmoo.o Neooo.o -m.¢ men.o om.mon m.ne

..mmoo.mo onns.om ..Hemoo.o ..Hmcoo.o 464.6 ~ma.o om.mon m.ms

mmmn.mmn mamm.mma meooo.o mmooo.o no¢.o m-.o oo.mon m.nm

mamm.sm 4HH.° Hun.o mn.msn «.Hm

omwn.oss mamm.onH mmmoo.o Huooo.o 4mm.o mn~.o mn.man n.m~

ssss.mme oHHm.H~H mnooo.o mmaoo.o nH~.o mmm.o mm.m~m ¢.~m
Amoaxwmos\ooc Imoammmfi\ooc .ndams .ndmzs .ndamx .admzx Ass a menace

>
acumen asaoBdAm+onoaunuAduz+uoo on» now even suxuausum n.n oases

.eanaeu eumamsousa as seen m>en hma menu mummomsm msHm> uaaao> Heaoa uome> zoa name a

 

 

Homm.os mmws.ms ossH.o em~.o m.~nn o.m4~
poms.osa omna.o s.~nn o.-~
mosm.om ammo.o 4.~nn m.os~

.mmsa.an mass.oma mmso.o mom.o e.~nn m.os~
vunm.os mann.o~H novo.o mme.o ”.mnn «.mma
mmmm.ns nmev.m~H anno.o mam.o «.mnn o.~¢a
ammo.om 4~.~.mss svao.o «Hm.o m.nnn «.mms
mao4.~n~ soum.sms onoo.o 4mm.o m.o.n m.mo

modxumoa\oo. mosxammwnoov Benz» ndazx as. 9 Isaac m

saunas oaoaeauasaz+uoo on» now seen suunsueum

N.m OHAOB

54

The results of the binary measurements are compared in
Figure 5.2 to liquid phase measurements reported by Cheong et
al. (Cheong et al. 1986). The two sets of measurements in the
liquid phase agree within the range of experimental error.

The results of the ternary measurements are compared in
Figure 5.3 to those of Zhang et al. (Zhang et al. 1988) for
the same system. The two sets of measurements do not appear
compatible. Composition isotherms plotted through Zhang's
data indicate much greater melting point depressions than
those observed in this work. Since insufficient information
is present in Zhang et al. '3 paper to determine the exact
conditions of the sample line during sampling, it is only
possible to speculate about the reason for this disagreement.
It should.be noted that the values reported from this work are
averages of multiple samples taken from alternating phases
over periods ranging from several hours to days, depending on
the time available for conducting the experiments in any given
day or week. This method should be more reliable than the
apparently single sample method employed by Zhang et al.
(1988).

In determining phase compositions, it was necessary to
calculate the number of moles of each component in each
sample. With this information and the calibration of the
sample loop volumes, it was possible to calculate values for
molar volumes of the samples. Details of the loop volume
calibration are detailed in Appendix G. The calculated values

are listed in Tables 5.2 and 5.3. The scatter of the volume

55

.Seumam ecuaenunmsc+uoo

may you mafia >qm macaw. mandamusmcmew modusmomaou owsvwa mo conducmaoo

con

 

 

 

    

 

 

. m m
can oo. o
h b b b > E“ P rlmingb 0.0
r
r so
T
r ...o
T
I 6.0
s to; ...: IGII I so
x x53 25. IUII
..m 6 9620 IOI. .
o;

 

« . n 055:

UOHOBJd alow

 
 
  
  
  
  
 
   

S-L-V Surface
Naphthalene-

Biphenyl-
co2 UCEP

UCEP

White and Lira

 

     
   
 

 

‘53 G K .5. _ I
Biph E Naph
€02
S-L-V Surface
Naphthalene-
Biphenyl-
CO2
Lu and
Coworkers
5;.
A
306-309K \‘
A
: I
I
l
Biph Naph

Figure 5.3 Comparison of data from this work and that of
Lu and co-workers.

57

data in Table 5.2 at higher pressures is a consequence of the
difficulty of sampling at higher pressures. From the degree
of the scatter, it is estimated that the volumes calculated
are accurate to within about 20%. This represents a lower
degree of accuracy than can be obtained by some other methods,
but, since all the information necessary to calculate the
molar volumes is collected in the course of obtaining the
composition data, and since it only requires a few additional
elementary calculations, it would be imprudent to neglect the
opportunity to glean this additional information.

As the pressure increases, the molar volume of the vapor
phase in the C02+naphthalene+biphenyl system becomes lower
than that of the liquid phase. This does not, however
indicate a phase inversion. Although the molar density of the
vapor phase becomes greater than the molar density of the
liquid, the mass density of the vapor remains greater than
that of the liquid.

Two of the data points at 305.8 K (at 73.8 and 74.5 bar)
have relatively low upper phase molar volumes. This is
evidence that these samples come from a second liquid phase.
Since the upper sampling port is out of the line of sight for
the cell window, it is possible that such a phase transition
may have occurred without being observed. This points out the
importance of being able to observe the phase being sampled
and the value of determining the molar volumes of the phases,

even if the values are only moderately accurate.

CHAPTER 6

PREDICTIVE MODELING

Experiments to determine solubilities and other phase
behavior in high pressure systems are difficult and expensive
to perform. .Accurate models and correlation schemes for high
pressure systems would provide a highly attractive
alternative, or at least supplement, to these experiments.
They would greatly reduce the number of experiments necessary
to reliably characterize a system by allowing more accurate
interpolation and extrapolation from limited data.
Experiments could be performed more efficiently if the phase
behavior could be predicted with sufficient accuracy. Models
can be used to indicate regions where phase transitions might
occur and the range of expected concentrations in each phase.
To date most models and correlations still have difficulty
accurately representing some important thermodynamic
properties of systems involving liquid, near critical, and
supercritical fluid phases (including solute-SCF behavior).
The problems lie primarily in two areas. First, dense fluid
phases are still incompletely understood. In dense fluids,
not only do the intermolecular forces of the nearest neighbor
shells become more important, but forces from more remote
shells exert significant influence on each molecule.
luolecular interactions become more complicated than the
'pmimarily binary interactions of diffuse gases. Because of

these difficulties, equations of state and correlations which

58

59

work well in the gas phase frequently fail when applied to
dense fluids. The most widely used cubic equations of state
(EOS's) do not always predict dense fluid volumes and
compressible with high accuracy. The implications of this
will be discussed shortly. Second, the close proximity of
individual molecules to each other in dense fluids allows
differences between like and unlike molecule interactions
greater impact. Mixing rules and correlations to describe the
impact of differences in molecular shape, size, polarity, and
polarizability are mostly empirical. Despite these
difficulties, some thermodynamic models can generate fairly
accurate qualitative or somewhat quantitative predictions of
high pressure phase behavior. (King et al. 1983, Paulaitis et
al. 1983, Hong et al. 1983, Adachi et al. 1986, Ziger and
Eckert 1983, Lemert and Johnston 1989) These fall into two
categories: using an equation of state for all fluid phases,
or using and equation of state for the vapor phase and an
activity coefficient model for the liquid phase. The equation
of state methods require minimal pure component data but do
not work well in mixtures without binary interaction
parameters. They tend to represent vapor phase thermodynamic
properties better than liquid phase properties.

The second approach requires more pure component data and
requires values for the liquid phase fugacity of the pure
components. This means finding methods to calculate a

hypothetical liquid fugacity above the pure component boiling

60
points and critical points for the supercritical fluid and
below the triple point for the organic solids.

The first approach was adopted for this work. The
Peng-Robinson and.translated Peng-Robinson equations of state
were tested and compared for their ability to predict
multi-component phase behavior.

Phase Equilibrium

The fundamental thermodynamic requirement for multi-phase

equilibrium is that the chemical potential of each component

in each phase be equal, i.e.

I1} = II. = II} “-1)

where “i is the chemical potential of component i, and a, fl,
and y are the phases. For a non-reacting system with solid,
liquid, and vapor phases, this equality of chemical potentials

is achieved when the following condition is satisfied:

(6.2)
ffIP,:r') = ff(P,T,x1) = f,"(P,T,y,) i = 1,2,3,...,n

where f1 is the fugacity of component i, the S, L, and V
superscripts denote the solid, liquid and vapor phases, P is
system pressure, T is system temperature, and xi and Yi are
the mole fractions of component i in the liquid and vapor

phases respectively.

61
Solid Fugacities
Since the solids used in this study do not ferm solid
solutions, all mole fractions are unity in the solid phases.

The fugacity of a pure solid is calculated from the equation

:3 = Ibiza (6.3)

where the fugacity coefficient ¢§ of the solid is found from

RT lanf . RV - gyp
If)» - 13.3.")... .11., - gr)... (6-4)

P
= ermpf“ + [(v- Ed?
P
P“!

.Most solids have very low saturation (sublimation) pressures,
so their vapors may be treated as ideal gases and the first
term of equation 6.4 becomes 0. Except at very, very high
pressures, solids are effectively incompressible: a pressure
of one kilobar only compresses iron by about 0.02%, copper by
about 0.2% and NaCl by about 0.5% (Sherman and Stadtmuller,
1987). Since the pressures being examined in this work are
even more modest, the volume in the second term of equation
6.4 may be assumed to be a constant with respect to pressure.

With these assumptions, equation 6.4 becomes:

62

 

S a _ P
RT 1m), = V[P - P5 ‘(TH RT mm (6.5)
which yields:
3 Pfl€(n 3“ [P- P1 MSOC(21)]) (6.6)

for the fugacity of the solids. ‘Vis is actually a function of
temperature, but for small temperature ranges, it may be
treated as a constant. If the values of the solid vapor
pressure as a function of temperature and the solid molar
volume are known accurately, the value of the solid fugacity
can be determined with high accuracy.
Liquid Fugacities

Liquid phase fugacities may be calculated by either the
fugacity coefficient method or the activity coefficient

method. In the fugacity coefficient method,

where oé is the fugacity coefficient of component i in the

liquid phase. ¢L is defined by the equation:

1
v1.
1- = 31'; - 31' - 6.8
RT 1m), f (612,) V dV an ( I
- Ritalin,

 

 

63

where R is the gas constant, T is absolute temperature, V is
total volume, mi and nj are the number of moles of components
1 and j respectively, and z is the compressibility factor.
Either actual data or an equation of state such as the
Soave-Redlich-Kwong or Peng-Robinson equations may be used to
solve the integral and determine the component fugacities.
Reliable P-T-V-x data, if available, would allow accurate
calculation of the liquid fugacities. Such data are usually
very scarce or non-existent. For this reason, it is usually
necessary to use an equation of state in the integration. The
accuracy of fugacities calculated using an equation of state
is heavily dependent on the ability of the equation to
correctly predict the P-T-V values of the system modeled.

An activity coefficient model may be used to calculate
the component activity coefficients in the liquid phase. In

the activity coefficient method fugacities are found from:

L _ .
ff 3 X1711;(P.: T,x1) f;L(T')exp[v_1(‘_;T_P_).] (6.9)

where yi‘ is the activity coefficient of component i in the
liquid and P' is the reference pressure where y? and f‘L are
calculated. The partial molar volume of pure component i in
the liquid, vi‘, is assumed independent of pressure. Where
pure component i cannot exist as a liquid at the stated
temperature, a correlation for the volume and fugacity of a

hypothetical superheated or subcooled pure liquid is used.

64

Such an approach has been used by Mackay and Paulaitis
(1979), Hess et al. (1986), and Lemert and Johnston (1989),
among others. Mackay and Paulaitis (1979) used an equation of
state to calculate the pure component liquid fugacities at the
reference pressure P’ and a temperature dependent Henry's
constant in the activity coefficient to fit the data. Hess et
al. (1986) developed a method for binary systems. Liquid
phase fugacities were calculated using regular solution
theory. The reference liquid phase fugacity for the light
component was found from the correlation of Chao and Seader
(1961). Lemert and Johnston (1989) used a method based in
part on approaches developed by McHugh and Krukonis (1986) and
Hess et al. (1986) which treat the subcooled liquid volume
and, to a lesser degree, the solubility parameters in the
regular solution theory model as adjustable parameters to fit
data. Lemert (1988) noted that the results of his model are
significantly affected by the values of the solubility
parameters used in the regular solution theory.
Vapor or Supercritical Phase Fugacities

Gases at high pressure and supercritical fluids can be
modeled as expanded liquids and treated with the same
equations as liquids (such as activity coefficient models)
(McHugh and Krukonis 1986) . To cover the entire pressure
range including lower pressures and densities with a single
equation, however, an equation of state approach with fugacity
coefficients would be thermodynamically consistent and the

least complex. Using an equation of state, the vapor and

65

supercritical phase fugacities would be calculated from the

equations:
fi" = y1¢¥p (6.10)
and
RT ln¢¥ s f(-§§) - R—J dV - anV (6.11)
V 1 T,V,nj¢h1

 

Kurnik et al. (1981, Kurnik and Reid 1982) used the
Peng-Robinson equation with one adjustable binary interaction
parameter to model solid-supercritical fluid solubility
behavior. They made the interaction parameter a function of
temperature to fit their data. Deiters and Schneider (1976),
and Chai (1981, Paulaitis et al. 1983) have used a second
adjustable parameter in the Redlich-Kwong-Soave and
Peng-Robinson equations of state to correlate data on phase
behavior of heavy solids with supercritical fluids. Johnston
and Eckert (1981, Johnston et al. 1982) used an augmented van
der Waals equation of state to predict solid solubilities in
SCF solvents with reasonable success. In this work, the phase
behavior was modeled with the Peng-Robinson and translated
Peng-Robinson equations of state with a single adjustable
interaction parameter.

As in the liquid phase, the accuracy of the calculated
fugacities depends on the accuracy of the volume, pressure,

and temperature values generated by the equation of state.

66
Pang-Robinson Equation of State

The Peng-Robinson equation of state

P= RT __ a(T,Io)

v-b v(v+b) +b(v-b) ‘6'”)

where v is the molar volume, may be used in equations 6.8 and
6.11 to determine liquid and vapor phase component fugacities

in a mixture. If the mixing rules

I III
a = ZEXIXJaij (6-13l
1-1 j-l .
a” = (l’kij)"a1aj (6.14)
I
b = xb (6.15)
f); i 1

are used, component fugacity coefficients can be calculated by

 

 

ln¢1=£51 (z-1) -1n(Z-B‘) + 324% -6,)1n :3. (fig; (6.16)

where

bi .. Tex/P91 ( )
— 7 6 . 17

 

67

 

2a“2
61 = a1 ngajl/2(1-ku) (6'18)
. _ 8P
A " W (6e19,
. . 2.12
.3 RT (6.20)

and kij is the binary interaction parameter for components i
and j. This equation of state has been found to work well in
predicting P—T-x-y values in vapor/liquid equilibria for many
systems. Liquid volumes predicted by this equation, however,
are still usually in error by several percent although they
are usually superior to those calculated by the
Redlich-Kwong-Soave equation of state which is of comparable
complexity.
Translated Pang-Robinson Equation of State
Peneloux and Rauzy showed that if the volumetric and
phase behavior of a fluid mixture are calculated by an
equation of state, certain translations may be made along the
xnolume axis without affecting the predicted phase equilibria
Of the fluid phases. The molar volume calculated by the
IJJmtranslated equation of state is denoted as v and the more
iiczcurate translated volume is denoted as V. This notation is
opposite that used by Peneloux and Rauzy but is more
<=<Insistent with the notation in the previous section of this

dissertation. A translation parameter c is defined such that

qsv-;c1x1=v-c (5'21)
-1
with

v, = (,1 - (:1 (6.22)
and

(,1 g .9}: (i=1,...,m) (6.23)
an
1 2315111.;

where all the ci's have constant values specific to each
component. When these volumes are substituted into the exact
thermodynamic relation for fugacity coefficients,

P 91

ln$1 =
0 RT

- .1 6.24
P)dP ( l

the more accurate translated fugacity coefficient (:31 may be

found from the relation:

1m), = 1m), - 51%; (6.25)

If the translated equation yields more accurate values for the
Volumes, then it would be expected to also give more accurate
Values for the fugacities as well. This equation does use one
more parameter than the original Peng-Robinson equation, but
the value of this parameter requires only pure component

liquid volume data. No additional mixture data are required.

69
Calculations and Comparison of Results
The Peng-Robinson and translated Peng-Robinson equations
of state have been compared and tested for their ability to
predict the thermodynamic properties and phase behavior of the
carbon dioxide+hydrocarbon binaries and ternaries measured
experimentally in this work. Details of the computational
schemes and the computer programs are contained in Appendices
C through F. Determination of parameter values is discussed
in Appendix G. Two types of calculations were attempted: 1)
P-T-x-y values were calculated along the SLV lines for the
C02+naphthalene, C02+biphenyl, and C02+phenanthrene binary
systems and along the SSLV lines for the
C02+naphthalene+biphenyl and C02+naphthalene+phenanthrene
ternary systems and 2) P-x-y values along isothermal SLV lines
in ternary systems. For the first calculations, values of all
other variables were solved for iteratively at fixed pressures
along the SLV or SSLV lines. For the second set of
calculations, temperature, pressure, and the component forming
the solid phase were specified and all remaining variables
were solved for iteratively. Both types of calculations were
carried out first using the Peng-Robinson EOS for the fluid
phases and then using the translated Pang-Robinson EOS for
those phases.
The P-T traces calculated for the binary and ternary
Systems are shown in Figures 6.1 through 6.5. The triple
Points for the pure solids (where the binary P-T traces should

begin) and eutectic temperatures for the solid/solid binaries

70

 

 

 

 

oThis work
700 - DiMcHugh (1981)
AMcHugh & Yogan (1984)
VCheong et al. (1986)
’ I DLemert & Johnston (1989)
' ——P-R E08
600 _ / .—-—Translated P-R E08
500 - I I
l
* l I
9 I
400 - /
’-‘=' i
a - .I
3 I
E 300 - .I
’ I
200 ' ,,
. *3
D s
100 - a'£‘>~
0 .\~\
.. W 0 ~\-
MU \.
D L l L TL—
330 340 350 360
TEMPERATURE (K)
Pigure 6.1 Predicted and measured SLV P-T traces for the

C02+naphthalene system.

71

 

fir I U U i U

D McHugh (1981) .
A McHugh and Yogan ( 1984)
V Cheong et al. (1986)
—' — P-R EOS J
-‘- Translated P-R EOS

I

700

U

600

I
~ - - — fl _ ~
~ ~
I

500 '
A

.. ‘ . / ,
g A '
e I

400 » . .
MI
9 . ,
3’: ’ V
‘6’
m 300

200

B
b

99
-’-——-—-——-.-

 

 

 

. ‘\~
100 7V av \~\
vu .
V \. d
I- q m \‘\
V D 7 ‘\~
0 J l j 1 gal I" d¥,
320 330 340 350
TEMPERATURE (K)
Figure 6.2 Predicted and measured SLV P-T traces for the

C02+biphenyl system.

72

 

 

 

 

 

. ' oThis work
700 / 4 Zhang et al. (1988)
' - —P-R EOS
. / —--Translated P-R E08
600 ' /
SUD ' r/ /
A I- I/ /
‘é / /
9 . /
400 '
.. / /
K I
:3 . / z’
a: . /
g 300 - / /
. /
I- 'l 2 /
200 L I 3 /
I 3 /
. \‘fial
100 - ‘Q-e
{29.0
. \\g:. o
\ 4
e\.
O n . - M .
350 360 370 380
TEMPERATURE (K)
lligure 6.3 Predicted and measured SLV P-T traces for the

C02+phenanthrene system.

73

 

 

 

 

I
'I
700 ~ / /
’ /
eon - l /
i ' O This work
/ ——P-R nos
I ' -"-Translated P-R E08

500 r l/
e ’/
g 400 ll
I./
U)
a ’/
E 300 - I /

./
200 ~ 1
Ion - l
o o}\\
o O .~;:;“‘”‘-m._‘
o a J W. I
290 300 310 320
TEMPERATURE (K)
Figure 6.4 Predicted and measured SSLV P-T traces for the

C02+naphthalene+biphenyl system.

74

#

 

 

 

 

O This work I /
700 . — — P-R nos /
-'-Translated P-R EOS , /
. '/ /
son . / /
. / /
500 '/ /
/ /
A y. r
‘2’ / /
9 I
400 - / /
ul
5 ' /
w /
m ' /
u.l
E300 - / /
. / /
200 ~ '/ /
//
100 " % log
_ lr-‘.§_
\
o %.$‘ ‘1: \
A A l l I
300 310 320 330
TEMPERATURE (K)
Figure 6.5 Predicted and measured SSLV P-T traces for the

C02+naphthalene+phenanthrene system.

75
(where ternary P-T traces should begin) are listed in Tables

6.1 and 6.2 for comparison.

 

Table 6.1
Pure Component Triple Points
Passenger—— W W
Biphenyl 342.37 8.4262x10’
Naphthalene 353.43 9.9938x10'
Phenanthrene 372.38 2.9043x10'4
Source: DIPPR data base
Table 6.2
Binary Eutectic Temperatures
9.1er W
Biphenyl and Naphthalene 312.55
Biphenyl and Naphthalene 312.85
Naphthalene and Phenanthrene 327.15
Naphthalene and Phenanthrene 321.25

Sources: Lee and Warner 1935
Gruberski 1961
Klochko-Zhovnir 1949
Rastogi and Varma 1956
The selection of parameter values is discussed in
Appendix G. In determining the best values for the
interaction parameters, the definition of what constitutes the
"best" fit of the data is subjective. For this work, the fit
<>f the predicted P-T curve to the experimental curve was used
as the criterion for selecting parameters. Using compositions
<>r volume data yields different parameters.
The original Peng-Robinson equation of state predicts the
IP-T traces of the binary and ternary systems qualitatively,

but using the volume translated Peng-Robinson equation can

improve the P-T trace predictions. Where the absolute value

76
of the pure component volume translation is relatively small,
i.e. naphthalene, the models yield slightly different results.
As the magnitude of c increases, the difference between the
models becomes more pronounced. The effect of c is manifest
in the P-T trace by the way the curves bend back. When c is
positive, i.e. for naphthalene and phenanthrene, the curves
bend back less. When c is negative, i.e. biphenyl, the trace
bends back more.

Both models over-predicted the pressures of the upper
critical end points of the C02+naphthalene and C02+biphenyl
systems and invariant points for the C02+naphthalene+biphenyl
and C02+naphthalene+phenanthrene systems. Based on the liquid
phase mole fractions reported and predicted for the
C02+phenanthrene system, it appears that this binary system
has not yet been measured up to its upper critical end point.
For naphthalene and phenanthrene, computational instabilities
and round-off errors caused the programs to terminate as the
critical end points were approached, but before they were
reached. Both equations predicted the upper critical end
point of the C02+naphthalene system to lie above the observed
UCEP. The translated Peng-Robinson equation predicted an
upper critical end point for the C02+biphenyl system about 50

bar above the 475 bar reported by McHugh and Yogan ( 1984) .
Predictions for both of the ternary systems indicate
fairly sharp changes in the slope at approximately the
Pressures where the apparent invariant points were observed

experimentally. Predictions above these points probably

77
represent metastable or unstable phases. The computer
programs written for this work did not include any tests for
such conditions.

The P-x-y traces calculated for the C02+hydrocarbon
binaries are plotted in Figures 6.6 through 6.8. The values
measured in this work and by Lu et al. are shown for
comparison. For naphthalene, the models predict similar
values at the lower pressures but diverge as the UCEP is
approached. The untranslated Peng-Robinson equation yields an
UCEP closer to the experimental value. For biphenyl, the
translated equation is slightly better, than the untranslated
equation, especially at the highest pressures. For
phenanthrene, the translated equation yields significantly
superior results to the untranslated equation.

The compositions predicted by the two equations of state

along the SSLV line and along the 310, 320, 330 and 340 K SLV
isotherms are plotted in Figures 6.9a and 6.9b. Data of Table
5.3 are also plotted in these figures for comparison. Except
at very high pressures, the plots are indistinguishable. Both
plots show better predictions in the right half of the diagram
where the solid phase is naphthalene than in the left half
where the solid phase is biphenyl. It should be noted that
both equations yield a predicted triple point for biphenyl
which is about 6 'C too high (compared to a 3 'C error for
naphthalene) . Consequently, the predicted composition of the
naphthalene+biphenyl eutectic is shifted toward a higher
biphenyl composition. This also results in a shift of the

78

 

 

 

 

700
O This work
I \ VCheong et al. (1986)
l \ :.:£;§.§i§...
600 - i .
i \
' I
' I! \\
' .I’ \\
E400 - I! \\
8' - l’ \\
8 l \
3:. 300 " I \ ‘\
0- - " o o \ ‘
1 vv \\
I (D O ‘
200 .I v \\
' 0 V“?
"éi
100 ‘Ky v
o \~-2~{
.‘\‘~
0 . . . . . . . . ‘S,
0.00 0.20 0.40 0.60 0.80 1.00
MOLE FRACTION
Figure 6.6 Predicted and measured P-x-y plot along the

SLV line for the C02+naphthalene system.

79

 

 

 

 

900 - I \ V ghlezoggéet al. (1986)
. ' \ ---Translated P-R E03
800 " l \
I- ' \
700 r \
. l
600 - l \
g . , \
e ! \
500 L ' I ‘ \
8 . \
a - . \
.. II \
g 400 " ' \ \
n. .I \ \
I \V
300 3’ \v)
I \
200 f \‘x
l
i \.
100 ' ‘dhi
_ \«q‘
«Isak
o A e 1 4 L - - ‘S
0.00 0.20 0.40 0.60 0.80 1.00
MOLE FRACTION
Figure 6.7 Predicted and measured P-x-y plot along the

SLV line for the C02+biphenyl system.

80

 

 

 

 

 

1000 ,
_ ‘ 4 Zhang et al. (1988)
, . —-P-R E08
900 , \ --—Translated P-R EOS
. |
800 . '\
700 l I
'l \ ’ \.
a; son 1' \ \
< I
m I.
v l \ \
g 500 I“ \ ‘
3 i \
In ' .
a: 400 \ \
n- 8
\ \
300 \ \
\ \33
200 l \ Q3
. \ .
100 \ {t
r \ Q‘
\‘34{
\\.
0 . - . . . . . 1 4 g
0.00 0. 20 0. 40 0.60 0.30 1.00
MOLE FRACTIDN
Figure 6.8 Predicted and measured P-x-y plot along the

SLV line for the C02+phenanthrene system.

   

81.

330 (C)

315.35

 

Figure 6.9

 

 

 

Biph-871 laphthalem;
(bl
3
340
340
Biphenyl . naphthalene
Comparison of equation of state phase

equilibrium predictions to experimental data.
SLV isotherms and SSLV lines were predicted
using ki values indicated in the text with
(a) the Peng-Robinson equation of state, and
(b) the translated Peng-Robinson equation of
state. Temperatures of the isotherms and data
are in Kelvin.

82
isotherms toward the naphthalene-rich side of the diagram
toward the experimental data on that side and away from the
observed compositions of the biphenyl-rich side. Since the
translated Peng-Robinson equation shows marked improvement
over the original Peng-Robinson equation for representing the
C02+phenanthrene system, it is expected that predictions from
the two equations for the C02+naphthalene+phenanthrene system
would show greater difference in their predictions with the

translated equation yielding the more accurate results.

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

Conclusions

A new experimental apparatus has been constructed which
can be used to study the phase equilibria of solids with
liquids and dense gases at high pressures. A method was also
devised to sample two equilibrium fluid phases at high
pressures. P-T-v-x-y data were measured along the upper
branch SLV line for the C02+naphthalene system and the values
of these data were compared to the P-T and P-T-x data obtained
by other researchers to validate the methods used in this
study. These measurements were also the first measurements of
the vapor phase compositions (y) and molar volumes (v) of this
system along the SLV line.

P-T data were measured along the upper branch SLV line
for the C02+phenanthrene system. P-T data were also measured
along the SSLV lines starting at the solid-solid eutectics of
the C02+naphthalene+biphenyl, C02+naphthalene-I-phenanthrene,
C02+naphthalene+acenaphthene, and C02+naphthalene+anthracene
systems. Except for the C02+phenanthrene system, for which
P-T data were reported (Zhang et al. , 1988) about the same
time the results reported here were first presented at the
1988 AIChE national conference (White and Lira, 1989) , none of
these systems had been previously measured. These
measurements were made up to apparent invariant points for the

coz+naphthalene+biphenyl and C02+naphthalene-I-phenanthrene

83

84
systems. The nature of the invariant points differs between
the two systems. In the C02+naphthalene+biphenyl system, the
SSLV line ends in a point where a second liquid phase is
formed. This probably occurs when the SSLV line intersects a
SLLV or SSLL line. In the C02+naphthalene+phenanthrene
system, the SSLV line seems to end in a point where the liquid
and vapor phases become identical (iue. a critical point).
Vapor and liquid composition data were also measured for seven
points along SLV isotherms of the C02+naphthalene+biphenyl
system. These measurements were not consistent with those
reported by Zhang et al., but it is believed that the results
reported here are more accurate.

Based on observations made during this work, to achieve
phase equilibrium within a reasonable period of time, both the
liquid and the vapor phases must be agitated. Although
diffusion in dense gases and supercritical fluids tends to be
much quicker than in liquids, unless these fluids are mixed,
concentration and thermal gradients will take substantial time
to dissipate. Thirty minutes of aggitation was adequate to
achieve a well mixed, isothermal system.

Also, based on observations during this work, sampling of
dense fluid phases where solid solubilities are a function of
pressure must be done carefully in order to get representative
samples. Pressure gradients between the equilibrium cell and
‘Uhe sample collection chamber (in this work, sample loops on
an IHPLC ‘valve) may' cause precipitation of solids, thus

altering the composition of a sample. Solids may also block

85
lines connecting the cell and the sample volume, preventing a
complete sample from being taken.

As demonstrated by the difference between the
C02+naphthalene+biphenyl and C02+naphthalene+phenanthrene
systems, binary data alone do not necessarily indicate some
important aspects of the phase behavior of multi-component
systems involving dense gases and supercritical fluids.
Although the constituent binaries of these two ternary systems
are very similar, the SSLV lines terminate in different types
of invariant points. The magnitude of melting point
depressions, and the location and nature of invariant points
may differ significantly between.multi-component systems even
when the constituent binaries are similar.

The Peng-Robinson and translated Pang-Robinson equations
were compared for their ability to accurately predict melting
point depressions and phase compositions along the upper
branch SLV lines for the C02+naphthalene, C02+biphenyl, and
C02+phenanthrene binary systems and.melting point depressions
along the SSLV lines for the C02+naphthalene+biphenyl and
C02+naphthalene-I-phenanthrene ternary systems. This is the
first time the translated Peng-Robinson equation has been
applied to such equilibria. The SLV isotherms predicted by
the translated and untranslated equations of state were also
compared for their ability to reproduce the SLV isotherm data
of the COZ-I-naphthalene-I-biphenyl system measured in this study.
The translated equation is at least as good as the original

Peng-Robinson equation of state for all systems examined in

86

this work. The improvement of the translated equation over
the original is most dramatic when the pressure is high or the
volume translation "c" for a pure component has a large
absolute value. Both models still fail to predict some
P-T-v-x-y values at the highest pressures. This is probably
due to insufficient accounting for molecular interactions
between unlike molecules, including differences in size and
shape. At the highest pressures, the molecules become more
densely packed, thus increasing the importance of these
di f ferences .

The molar volume values obtained by the methods of this
work are accurate to only about 120%. Although this does not
represent an improvement over other available methods for
determining phase volumes, the information is easy to extract
from the data taken in the course of finding the phase
compositions and does offer a quick means to obtain additional
useful information of fair accuracy about the systems being
studied.

Recommendations

Based on the results of this work, three modifications of
the experimental apparatus and several types of experiments
are suggested. The apparatus modifications should make both
melting point determinations and sampling easier. The
experiments would facilitate a better understanding of the
complex behavior of solute-supercritical fluid systems.

The current view cell has blind spots where the phase

behavior cannot be observed and is sometimes difficult to

87

light adequately. The first apparatus modification entails
building a high pressure view cell with two windows opposite
each other instead of at right angles as in the current cell.
The significant density and light scattering ability of the
liquid phase makes it difficult to get adequate lighting into
the current view cell to observe phase changes such as the
precipitation of solids or formation of additional liquid
phases. To get maximum improvement in lighting, the distance
between the windows should be kept as small as possible. One
limiting factor would be allowing sufficient space to insert
a mechanism similar to the one used in the current view cell
to agitate both phases. Since magnetic stir bars of
sufficient size and strength to couple well with a magnetic
stirrer are usually at least 1 inch long, this probably
represents the smallest practical distance between the
windows.

The current apparatus requires a fairly involved
procedure to extract samples from the phases alternately. The
second apparatus modification would be to use two 6-port HPLC
valves for sampling instead of one 10-port valve. This would
simplify sampling by eliminating the intermediate steps of
flushing the lines and non-active sample loop during sampling
to avoid contaminating the active sample loop. It would also
allow the phases to be sampled more nearly simultaneously
instead of alternately. Since the temperature within the bath
May be too hot to allow putting a hand into the bath to turn

the sample valves, long handles must be attached to the valves

88
to permit them to be switched from outside the bath. The
sample ports should therefore be located such that the HPLC
valves are not together on the same side of the cell.

Because a water bath is used, the experiments are limited
to the range of temperatures for which water is a liquid at
atmospheric pressure. The third change in the experimental
apparatus would be to replace the water in the temperature
control bath with a heat transfer fluid which can reach higher
and lower temperatures than water without freezing and
boiling. The fluid should be chosen such that it does not
attack o-ring materials or corrode metals. It also ought to
be one which can be thoroughly cleaned from the cell surface
when the cell is removed for reloading since even small
amounts of contaminants can alter the phase behavior of the
cell contents.

The first extra measurements ought to be designed to
extend the P-T trace of the C02+phenanthrene line to the upper
critical end point. These experiments would probably have to
be done in a capllary due to the high pressures necessary.
This would permit better comparison of potential models to the
data.

The second set of measurements should be designed to more
completely characterize compositions along the three phase SLV
isotherms of the C02+naphthalene+biphenyl system. This will
require preparing samples of many different compositions and
adjusting them isothermally to the pressure where solids just

begin to form before sampling.

89

The third set of measurements should be designed to
determine the nature of the invariant points reached in this
work for both the C02+naphthalene+biphenyl and the
C02+naphthalene-I-phenanthrene systems.

A fourth set of recommended experiments would involve
studying the C02+biphenyl+acenaphthene system. Since the
eutectic temperature of the biphenyl+acenaphthene binary is
lower than that of the biphenyl+naphthalene binary, the
ternary eutectic with CO2 should also be lower. The SSLV line
of this system would almost certainly intersect a SSLL line
with a C02 rich liquid forming the second liquid.

It would also be illuminating to examine the accuracy of
the translated Peng—Robinson equation when applied to
multi-phase systems with supercritical solvents other than
C02. Ethane and ethylene are supercritical at relatively mild
temperature and pressure conditions. Since some data already
exist for multi-phase systems including these components (see
Table 2.1), it is suggested these be examined next. Such
studies are necessary to determine whether volume translation
offers any improvements for systems with solvents for which
the original Peng-Robinson equation provides better or worse
predictions than it does for C02 systems.

To expand the understanding of supercritical fluids and
facilitate evaluations of phase equilibrium prediction schemes
such as the one just mentioned, additional P-T-v-x-y
measurements should be made along multi-phase lines of systems

with ethane and ethylene. Several classes of compounds ought

90
to be included in these studies, such as: long chain and
branched alkanes, heavy alcohols, aromatics, ketones, and
esters. Each of these types of compounds would provide
information about the effects of different functional groups
on the phase behavior of solid-SCF systems. The compounds
should be chosen such that their triple points are well above

the critical temperature of the supercritical solvent.

APPENDICES

APPENDIX A

GC CALIBRATION

The GC is calibrated twice --- once for determining the
amount of naphthalene relative to biphenyl and the second time
to determine both naphthalene and biphenyl concentrations
relative to acenaphthene. Calibration standards are prepared
by weighing out each component for the sample solution in the
volumetric flask used as a sample container and filling the
flask to the volume line with toluene to dissolve the solids.
All solids are weighed out to within 10.0003 grams on a
Sartorius R300S balance. A clean stir bar is added to each
sample and they are placed on a magnetic stirrer for at least
an hour to assure that each solution will be homogeneous. The
area of each component peak divided by the area of the peak
for the 1.8. (internal standard) is determined for at least
five different concentrations over a two order of magnitude
range. The concentration of naphthalene or biphenyl as a
function of the area ratio and concentration of the 1.8. is
then determined by a least squares fit of the data to an
equation of the

form:

 

component mass = m1 solutionx 9 I'S', xslopexIfi (1L1)
ml solution

91

92
The compositions of the samples are analyzed on a Perkin-Elmer
8500 gas chromatograph using an Alltech 10 m x 0.53 mm Bonded
FSOT RSL-50 column with a 6 inch length of uncoated 0.53 mm

negabore tubing as a pre-column condensing section. The GC

settings were as follows:

93

secrros 1 cc coumnon*
l 2 3
Oven Temp ('C) 40 100 115
Iso Time (Min) 4.0 7.5 3.0
Ramp Rate ('C/Min) 7.5 30.0
HWD 1 Range Off FID 2 Sens High
HWD 1 Polarity B-A
INJ 1 Temp Off INJ 2 Temp 300 ’C
DET 1 Temp 200 ’C DET 2 Temp 310 ’C
Flow 1 10 ml/Min Pressure 3 5.0 psig
Flow 2 10 ml/Min Carrier Gas 2 He
Carrier Gas 1 He
DET Zero On Equilib Time 0.0 Min
Initial DET 2 Total Run Time 23.0 Min
SECTION 2 TIMED eveums**
Time Exes;
-1.00 Relay 1 On
0.20 Relay 0 On
SECTION 3 DATA naunnrne**
D l E 0 s O ! 0 E !
Start Time 10.00 Min Calc Type %
End Time 23.00 Min Area/Ht Calc Area
Print Tol 0.0000
Width 5 Output
Skim Sens 1 Screen Yes
Baseline Corr B-B Printer No
Ext Dev Yes
DET 1 Area Sens 50
DET 2 Area Sens 121
DET 1 Base Sens 4
DET 2 Base Sens 6

**

The Perkin-Elmer 8500 gas chromatograph was configured
with dual packed columns and a hot-wire detector in
position 1 and the single column (megabore or capillary
column) connected to an FID detector in position 2. All
analyses for this work were done with the position 2
hardware (column and detector).

The "Timed Events" and "Data Handling" parameters given
are specific to the instrument used and the configuration
of that instrument. They are given here to document the
exact conditions of the analysis as well as to enable
duplication of the method.

APPENDIX B
SAMPLE LOOP VOLUME DETERMINATIONS

The equipment configuration used to determine the volume
of the two sample loops was identical to that used in the
composition measurements except that the sample loops were
connected directly to a high pressure tank of helium.

Sample loop volumes were calculated using the equations:

V

nv (Ploop,'I‘) (a.B)

n = Pambientvfinal

.8
RT (7 )

with vfinal the volume of the helium at atmospheric pressure.
The molar volumes of helium at elevated pressures were

calculated from the viral coefficients calculated from the

data of Wiebe. Gaddy and Heins in Ihe.!irial.§eefficients_9f
Bure_§a§ea_and_uixtures by Dymond and Smith (1980)-

94

 

 

95

Data for Velume Determination of Sample Loop 1

Final
Volume
.1221.

3.65
3.65
3.65
2.75
2.85
2.85
2.85
4.20
4.25
4.20
4.25
5.75
5.75
5.75

average calculated volume

Moles
Helium

1.485
1.485
1.485
1.119
1.160
1.160
1.160
1.709
1.729
1.709
1.729
2.339
2.339
2.339

v
Helium

cczsmel
336.861
336.861

337.158

442.701

437.712

435.190

432.697

297.815

296.769
295.637
295.637
222.076
222.112
222.112

standard deviation

% std. deviation

Loop

Volume
.1221._
.050026
.050026
.050070
.049556
.050762
.050469
.050180
.050911
.051319
.050521
.051123
.051954
.051953
.051953

.050773
.000766

1.508690

Data for Volume Determination of Sample Loop 2

 

Table B.1
Loop
Temperature Pressure
(Kl
296.75 75.8421
296.75 75.8421
296.75 75.7731
296.75 57.2263
296.85 57.9158
296.85 58.2605
296.85 58.6052
296.75 86.1842
296.85 86.5289
296.85 86.8736
296.85 86.8736
296.85 117.2105
296.90 117.2105
296.90 117.2105
Table B.2
Loop
Temperature Pressure
(K) (par)
296.85 56.5368
296.85 57.2263
296.85 57.9158
296.90 58.2605
296.90 58.6052
296.90 83.4263
296.85 84.1158
296.85 84.8052
296.90 84.8052
296.90 119.2789
296.90 119.2789
296.85 119.6236
NOTE:

Final
Volume
(9c)
5.70
5.70
5.70
5.80
5.80
8.45
8.50
8.50
8.50
12.10
12.10
12.10

average calculated volume

Moles
Hel'um
0’4

.31...

2.321
2.321
2.321
2.361
2.361
3.439
3.460
3.460
3.459
4.944
4.944
4.945

v
Helium

448.106

442.846
437.712
435.261
432.768
307.430
304.954
302.568
302.617
218.457
218.457
217.826

standard deviation

% std. deviation

Ambient atmospheric pressure =
tables.

Loop
Volume
..LEQL.
.103994
.102773
.101582
.102766

.102178

.105721
.105508
.104683

.104682

.108001
.108001
.107707

.104800
.002169

2.069595

1.004 bar for both

APPENDIX C

ITERATION SCHEME FOR SLV AND SSLV LINE DETERMINATIONS

 

_. v1 (P-Pf“) '
.3: ..fIS'I‘gacem ””" RT

i4 ..iGuess Y; valuesl

 

 

 

 

 

 

 

 

 

 

@1861... an «31‘
I - s

   
 

 

 

   

 

10 . Guess xi values
11. Calculate all 4)? '

 

 

 

 

 

‘ . .. .. A: .
17.2. If An"=“"<o then AT=-————‘°—1d

. A,”d 2,

17b. If [Ane,|>|Aoml then AT=-AT°M'
17C. fiToIdeT , , , ,

 

 

 

 

 

 

[1.81. 13x, and y valuesfound'for- P|

19....NeXt P ?

 

96

Notes:

1)

2)

3)

4)

5)

97
The programs in Appendix D are used to make these
calculations.
x1 and Y1 are the mole fractions of the solvent in
the liquid and vapor phases respectively.
If cross parameters (kij for example) are used for
the calculation of the ¢¥ and o? values (steps 5
and 11), they must be entered during the execution
of the program.
The x iteration scheme (steps 10 through 17) is
adapted from. several sources in ‘the literature
including Henley and Seader (1981) and McHugh and
Krukonis (1986).
This iteration scheme uses the following programs
from Appendix D:

Main
Program - This is the first program listed in

Appendix D. It follows the outline at the
beginning of this appendix (C) and calls
various subroutines to get initial and

intermediate data.

INPUT - This subroutine reads initial variable
values.

FIXXY - This subroutine returns values for mole
fractions weighted by the initial
guesses.

SFUG - This subroutine calculates the fugacities

of solid phases.

VEOS

LEGS

CUBIC

98

- This subroutine calculates vapor phase

fugacity coefficients. There are two
versions of this in Appendix D. The
first uses the original Peng-Robinson
308; the second uses the translated
Peng-Robinson EOS.

This subroutine calculates liquid phase
fugacity coefficients. There are two
versions of this in Appendix D. The
first uses the original Peng-Robinson
EOS; the second uses the translated
Peng-Robinson EOS.

This subroutine solves a cubic polynomial
for the three real or imaginary roots.
It is required in the subroutines VEOS

and LEGS.

C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)CI€)C)C)C)C)C)C)C)C)C)C)C)CIC)C)C)C)C)C)C)CICWO

APPENDIX D

COMPUTER CODE FOR CALCULATING SLV AND SSLV LINES

******************************************************************
* THIS PROGRAM CALCULATES THE COMPOSITION AND THE P,T TRACE OF *
* THE THREE OR FOUR-PHASE LINE (SLV OR SSLV) FOR A BINARY OR *
* TERNARY SYSTEM WITH ONE LIGHT (I.E. GAS AT AMBIENT CONDITIONS) *
* COMPONENT AND ONE OR TWO HEAVY (I.E. SOLID AT AMBIENT *
* CONDITIONS) COMPONENTS. *
* *

COMPONENT 1 IS CHOSEN TO BE THE LIGHT COMPONENT.
******************************************************************

******************************************************************

ADELTAI ABSOLUTE VALUE OF DELTAl (|DELTA1|)
ADELTA2 ABSOLUTE VALUE OF DELTA2 (lDELTAZl)
ANT(I,J) ANTOINE COEFFICIENTS OF COMPONENT I

C(I) VOLUME TRANSLATION FOR COMPONENT I

DELTAl NEW VALUE OF (FUGV - FUGL)

DELTA2 OLD VALUE OF (FUGV - FUGL)

DELTAT INCREMENTAL CHANGE TO T FOR THE NEXT ITERATION

DELMIN THE SMALLEST REASONABLE ABSOLUTE TEMPERATURE
INCREMENT

DELX THE CHANGE IN X(I) FROM THE LAST ITERATION LOOP

DFG(I) DOUBLE PRECISION FG(I)

DHF(I) MOLAR HEAT OF FUSION OF PURE COMPONENT I AT ITS
NORMAL MELTING POINT (CAL/G-MOLE)

DI MAXIMUM ALLOWABLE PRESSURE INCREMENT FOR THE NEXT
LOOP

DINCR PRESSURE INCREMENT FOR THE NEXT LOOP (UNITS OF BAR)

DNEWX(I) NEXT PREDICTED VALUE FOR X(I) BASED ON THE PHI
(FUGACITY COEFFICIENT) VALUES CALCULATED FROM THE
OLD X(I) VALUES

DOLDX VALUE OF X(I) FROM THE LAST ITERATION - USED TO
KEEP THE PROGRAM FROM CHASING AFTER A VALUE OF
X(I) IN A REGION WHERE IT WILL NEVER FIND A
SOLUTION (X(I) INCREASES MONOTONICALLY WITH
INCREASING PRESSURE.)

DP DOUBLE PRECISION P

DP1 PRESSURE (IN BAR) FOR THE FIRST CALCULATION

DPHI(I) FUGACITY COEFFICIENT OF COMPONENT I

DRATIO(I) RATIO Y(I)/X(I) - USED TO CHECK FOR APPROACH TO
THE CRITICAL POINT - USUALLY THE UPPER CRITICAL
END POINT (UCEP)

DPTOP THE TOP PRESSURE FOR WHICH CALCULATIONS WILL BE
PERFORMED
DSUMX SUM OF THE X VALUES PREDICTED BASED ON THE

FUGACITIES CALCULATED IN THE SOLID AN VAPOR PHASES
- WHEN THE CORRECT TEMPERATURE HAS BEEN FOUND,

E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E
E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

99

OOOOOOOOOOOOOOOOOO00000000000OOOOOOOOOOOOOOOOOOOOOOOO

i * i * * $ $ * i i i i i * i i * $ $ $ $ $ fi * fi * i i i i * i * $ $ * * fl * fi * i * $ * *

DSUMY

DX(I)
DXOLD

DY(I)
DZ
FG(I)

FUGL
FUGV
I

K(I,J)

OLDT

OMEGA(I)

LU

100

THE X VALUES WILL SUM TO I

SUM OF THE Y VALUES OF THE SOLID COMPONENTS IN THE
VAPOR PHASE BASED ON THEIR SOLID PHASE FUGACITIES
DOUBLE PRECISION X(I)

VALUE OF DX(1) CALCULATED AT THE LAST PRESSURE -
DX(1) SHOULD KEEP INCREASING AS THE PRESSURE
INCREASES, SO ANY GUESS FOR X1 LOWER THAN THAT AT
THE LAST PRESSURE IS TOO LOW AND DX(1) IS RESET TO
DXOLD AS THE LOWER BOUND - USING THIS STRATEGY
HELPED KEEP THE SEARCH FOR THE LIQUID COMPOSITION
IN A FEASIBLE RANGE SO THE PROGRAM WOULD NOT CRASH
DOUBLE PRECISION Y(I)

DOUBLE PRECISION COMPRESSIBILITY FACTOR

FUGACITY OF PURE COMPONENT I IN THE GAS OR SCF
PHASE

LIQUID PHASE PARTIAL MOLAR FUGACITY OF COMPONENT 1
VAPOR PHASE PARTIAL MOLAR FUGACITY OF COMPONENT 1
COMPONENT NUMBER

INTERACTION PARAMETER FOR COMPONENTS I AND J

T VALUE USED IN THE PREVIOUS ITERATION - USED TO
KEEP TRACK OF WHICH WAY T IS BEING ADJUSTED AS THE
ITERATIONS PROCEED

PITZER ACENTRIC FACTOR OF COMPONENT I

MOLAR VOLUME OF LIQUID MIXTURE (CC/G-MOLE)

NUMBER OF COMPONENTS IN THE SYSTEM

SYSTEM PRESSURE (UNITS OF BAR)

PRESSURE FOR THE FIRST LOOP (UNITS OF BAR)

THE CRITICAL PRESSURE OF PURE COMPONENT I IN UNITS
OF BAR

PRESSURE IN psia - CALCULATED BUT NOT USED IN THIS
VERSION OF THE PROGRAM

PRESSURE FOR THE LAST LOOP (UNITS OF BAR)

SYSTEM PRESSURE (UNITS OF ATM)

SYSTEM TEMPERATURE IN UNITS OF KELVIN

THE CRITICAL TEMPERATURE OF PURE COMPONENT I IN
UNITS OF KELVIN

SYSTEM TEMPERATURE IN DEGREES CELSIUS

NORMAL MELTING POINT OF PURE COMPONENT I (KELVIN)

THE CRITICAL VOLUME 0F PURE COMPONENT I (CC/G-MOLE)
MOLAR VOLUME OF PURE LIQUID COMPONENT I (CC/G—MOLE)

MOLAR VOLUME OF PURE SOLID COMPONENT I (CC/G-MOLE)
VOLUME OF VAPOR MIXTURE (CC/G-MOLE)

THE MOLE FRACTION OF COMPONENT I IN THE LIQUID
PHASE

THE MOLE FRACTION OF COMPONENT I IN THE GAS OR
SCF PHASE

* $ $ $ $ fi * $ $ * * $ * $ $ $ $ $ * $ * $ $ $ $ $ * * $ $ $ $ * $ $ $ * $ $ $ * $ $ $ $ $

******************************************************************

******************************************************************
* NOTE: SOME OF THE ARGUMENT LISTS FOR SOME OF THE SUBROUTINES

*
*
*

*

CALLED IN THIS MAIN PROGRAM MAY CONTAIN VARIABLES WHICH *
ARE NOT USED IN THIS PROGRAM.

*
*

101

THIS IS A RESULT OF MY ATTEMPTS TO MAKE THE PROGRAM AND
SUBROUTINES FLEXIBLE ENOUGH TO ALLOW EASY CHANGE-OVER TO
OTHER ALGORITHMS, EQUATIONS OF STATE, ETC. WITHOUT
REWRITING THE ENTIRE CODE.

IF A VARIABLE LISTED IN THE CALLING ARGUMENT OF A
SUBROUTINE CALLED HERE IS NOT USED ELSEWHERE IN THE
PROGRAM, DO NOT GET CONCERNED, IT PROBABLY WAS NEEDED
WHEN THAT SUBROUTINE WAS CALLED IN A DIFFERENT PROGRAM
OR IS REQUIRED WHEN A DIFFERENT EQUATION OF STATE IS
USED.

*fl-fl'fl-fi-Ififl-fifl-fifl-
fix-M-fi-M-X-M-X-fl-X-M-

0000000000000

DIMENSION ANT(3,3),C(3),DHF(3),FG(3),K(3,3),OMEGA(3),PC(3)
DIMENSION TC(3),TM(3),VC(3),VL(3),VS(3),X(3),Y(3)
REAL LV
DOUBLE PRECISION ADELTA1,ADELTA2,DELMIN,DELTA1,DELTA2,DELx,DFC(3)
DOUBLE PRECISION DI,DINCR,DNEWX(3),DP,DP1,DPHI(3),DRATIO(3),DSUMY
DOUBLE PRECISION DPTOP,DX(3),DXOLD,DY(3),DZ
OPEN (UNIT - 5, STATUS - 'UNKNOWN')
OPEN (UNIT - 6, STATUS - 'UNKNOWN')
OPEN (UNIT - 17, STATUS - 'NEW', FILE - 'OUTPUT.DAT')
CALL INPUT (ANT,C,DHF,K,NC,OMEGA,PC,PTOT,T,TC,TM,VC,VL,VS,X,Y)
CALL FIXXY (NC,DX,DY,X,Y)
DOLDX - 1.DO
WRITE (6,70)
READ (5,*) DP1
WRITE (6,74)
READ (5,*)DPTOP
WRITE (6,78)
READ (5,*)DINCR
WRITE (17,86)
WRITE (17,90)
DI - DINCR
DP - DP1
WW****H***WWMWW*****
THE NEXT STATEMENT IS INTENDED TO GIVE A REASONABLE FIRST GUESS *
FOR THE FUGACITY OF THE LIGHT COMPONENT FOR THE FIRST ITERATION. *
WWW
DFG(I) - DP1
OLDT - T + O.ZDO*DINCR
DELMIN - (.002)*DINCR
300 DELTAT - (T - OLDT)
WWWWWWWWM
* THE NEXT 4 LINES ARE TO PREVENT SUCH A SMALL INITIAL INCREMENT IN *
* THE TEMPERATURE GUESS THAT CONVERGENCE BECOMES A PROBLEM. *
*WWW*****H****mmmmm*m**m*******
IF (ABS(DELTAT).LT.ABS(DELMIN)) THEN
IF (DELTAT.CE.0.) DELTAT - DELMIN
IF (DELTAT.LT.O.) DELTAT - - DELMIN
ENDIF
‘OLDT - T
DELTAz - -100.D0

C)C)€3C}
X-

I”

0000

102

ADELTAZ - DABS(DELTA2)
400 CALL SFUG(ANT,DFC,NC,DP,T,VS)
CALL VEOS(C,DFG,K,NC,OMEGA,DP,PC,DPHI,T,TC,VV,DY,DZ)
DSUMY - 0.0DO
DO 420 I - 2,NC
DSUMY - DSUMY + DY(I)
420 CONTINUE
DY(I) - 1.D0 - DSUMY
DFG(I) - DY(1)*DPHI(1)*DP
450 CALL LEOS(C,DFG,K,NC,OMEGA,DP,PC,DPHI,T,TC,LV,DX,DZ)
DSUMX - 0.0D0
DO 500 I - 1,NC
DNEWX(I) - DFG(I)/DPHI(I)/DP
DSUMX - DSUMX + DNEWX(I)
500 CONTINUE
DELX - DABS(DNEWX(1)-DX(1))/DX(1)
DX(1) - (DX(1)+DNEWX(1))/2
IF (DX(1).EQ.DXOLD) THEN
WRITE (6,50)
50 FORMAT (X,'X(1) NOT CHANGING')
CWWWWWW
C * IF X(I) IS NOT CHANGING BUT THE CONVERGENCE CRITERIA HAVE NOT BEEN *

C * MET, THIS BRANCH WILL PREVENT AN ENDLESS LOOP. *
c **********************************************************************
STOP
ENDIF

IF (DX(1).LT.DXOLD) DX(1)-DXOLD
DO 600 JJ-2,NC
DX(JJ) - (1 Do - DX(1))*DNEWX(JJ)/(DSUMX-DX(1))
600 CONTINUE
IF (DELX.GT.2.SD-4) GOTO 450
DELTAI - DELTA2
DELTA2 - 1.DO - DSUMX
ADELTAI - DABS(DELTAI)
ADELTAz - DABS(DELTA2)
IF (ADELTA2.CE.1.D-O3) THEN
IF (DELTA2/DELTA1.LT.O.DO) THEN
DELTAT - -DELTAT/2.DO
ELSE IF(ADELTA2.CT.ADELTA1) THEN
DELTAT - ~DELTAT/2.DO
ENDIF
T - T + DELTAT
GOTO «00
ENDIF
1000 PPSIA - DPTOT*14.696
TDEGC - T - 273.15
DOLDX - DX(1)
WRITE (17,92) DP,T,DX(2),DX(3),DY(2),DY(3)
WRITE (6,94) DP,T
DO 1200 I-1,NC
DRATIO(I) - DY(I)/DX(I)
1200 CONTINUE
DO 1300 I - 2,NC

00000

103

IF (DRATIO(I).CT.5.0D-02) DI 5.0
1300 CONTINUE
DO 1310 I - 2,NC
IF (DRATIO(I).CT.8.0D-02) DI - 2.5
1310 CONTINUE
DO 1320 I - 2,NC
IF (DRATIO(I).GT.1.1D-01) DI - 1.0
1320 CONTINUE
D0 1330 I - 2,NC
IF (DRATIO(I).GT.1.3D-01) DI - 0.5
1330 CONTINUE
DO 13h0 I - 2,NC
IF (DRATIO(I).GT.2.0D-01) DI - 0.25
13h0 CONTINUE
DO 1350 I - 2,NC '
IF (DRATIO(I).GT.3.0D-01) DI - 0.1
1350 CONTINUE
D0 1360 I - 2,NC
IF (DRATIO(I).GT.3.SD-01) DI - 0.05
1360 CONTINUE
IF (DI.LE.DINCR) DINCR - DI
IF (DP.EQ.DPTOP) THEN
GOTO 2000
ELSE
IF (DP.EQ.DPl) THEN
DP - DINCR
1500 IF (DP.GT.DPl) GOTO 300
DP - DP + DINCR
GOTO 1500
ELSE
DP - DP + DINCR
IF (DP.GT.DPTOP) DP - DPTOP
GOTO 300
ENDIF
ENDIF
2000 CONTINUE
70 FORMAT (1X,'INPUT LOWEST PRESSURE IN BAR')
74 FORMAT (1X,'INPUT HIGHEST PRESSURE IN BAR')
78 FORMAT (1X,'INPUT THE SIZE OF THE PRESSURE INCREMENT IN BAR')

82 FORMAT (1X,'INPUT K(',Il,',',I1,')')

86 FORMAT (X,'PRESSURE MELTING POINT')

90 FORMAT (X,' (BAR) (K) X2 X3 Y2
& Y3')

92 FORMAT (X,F8.3,2X,F13.5,4(2X,G9.4))
93 FORMAT (X,3(G15.8,5X)/)
94 FORMAT (1X,'THE MELTING POINT AT ',F8.3,' BAR IS ',G15.7)

END

WWWWMW**
* SUBROUTINE INPUT *
WWMWEEWWMEEEEEE
* ANT(I,J) ANTOINE COEFFICIENTS FOR COMPONENT I FOR VAPOR *
* PRESSURE IN UNITS OF BAR *

0000000000000000000000000000

21(30

104

* C(I) VOLUME TRANSLATION VALUE FOR COMPONENT I *
* DELTA(I) HILDEBRAND SOLUBILITY PARAMETER OF COMPONENT I IN *
* (CAL.CM**3)**l/2 *
* DHF(I) HEAT OF FUSION OF COMPONENT I IN CAL./G-MOL *
* I AND J COMPONENT # SUBSCRIPTS *
* JUNRI DUMMY VARIABLE To BYPASS DATA SET IF NAME2 DOES *
* NOT EQUAL NAME1 *
* JUNR2 SAME DESCRIPTION AS JUNRl *
* JUNR3 SAME DESCRIPTION As JUNKI *
* JUNRA SAME DESCRIPTION AS JUNKI *
* R(I,J) INTERACTION PARAMETERS FOR THE I,J COMPONENT PAIR *
* NAME1 NAME OF COMPOUND CHOSEN *
* NAME2 NAME OF COMPOUND FOR WHICH DATA IS LISTED IN DATA *
* FILE --- COMPARED WITH NAME1 TO SEE IF IT IS THE *
* DESIRED SET OF DATA *
* NC NUMBER OF COMPONENTS IN THE SYSTEM *
* OMEGA(I) PITZER ACENTRIC FACTOR OF COMPONENT I *
* PC(I) CRITICAL PRESSURE OF COMPONENT I IN ATM *
* PTOT SYSTEM PRESSURE IN ATM *
* T SYSTEM TEMPERATURE IN KELVIN *
* TC(I) CRITICAL TEMPERATURE OF COMPONENT I IN KELVIN *
* TM(I) NORMAL MELTING POINT OF COMPONENT I IN KELVIN *
* VC(I) CRITICAL VOLUME OF COMPONENT I IN CM3 *
* VL(I) MOLAR VOLUME OF LIQUID COMPONENT I IN CM3/G-MOL *
* VS(I) MOLAR VOLUME OF SOLID COMPONENT I IN CM3/G-MOL *
* X(I) MOLE FRACTION OF COMPONENT I IN THE LIQUID PHASE *
* Y(I) MOLE FRACTION OF COMPONENT I IN THE VAPOR PHASE *

******************************************************************
SUBROUTINE INPUT (ANT,C,DHF,K,NC,OMEGA,PC,PTOT,T,TC,TM,VC,VL,VS,
&X,Y)
DIMENSION ANT(3,3),C(3),DHF(3),DELTA(3),OMEGA(3),PC(3),TC(3)
DIMENSION TM(3),VC(3),VL(3),VS(3),X(3),Y(3)
REAL K(3,3)
OPEN (UNIT - 5, STATUS - ’UNKNOWN')
OPEN (UNIT - 6, STATUS - 'UNKNOWN')
OPEN (UNIT - 10, STATUS - 'OLD', FILE - 'PHASE5.DAT')
OPEN (UNIT - 17, STATUS - 'UNKNOWN', FILE - 'OUTPUT.DAT')
WRITE(6,80)
READ (5,90) NC
WRITE(6,82)
READ (5,91)T
DO 200 I - 1,NC
WRITE(6,83) I
READ (5,92) NAME1
WRITE(17,88) NAME1
READ (10,92) NAME2
IF (NAME1.EQ.NAME2) THEN
READ (10,93) OMEGA(I),PC(I),TC(I),VC(I)
READ (10,93) DELTA(I),VL(I),VS(I),TM(I)
READ (10,93) DHF(I),X(I),Y(I),C(I)
READ (10,94) ANT(I,1),ANT(I,2),ANT(I,3)
ELSE
READ (10,96) JUNK1,JUNK2,JUNK3,JUNK4

gr

 

 

 

C3C)C)C)C)C)()C)C)C)C)C)C)

200

300
400
80
81
82
83

9'9‘9‘

86
88
90
91
92
93
94
96

105

GOTO 100

ENDIF
CONTINUE
DO 400 I - 1,NC-1
DO 300 J - 1,NC
IF (I.EQ.J) THEN

K(I,J) - 0.
GOTO 300
ENDIF

WRITE (6,86) I,J
READ (5,*) R(I,J)
R(J,I) - R(I,J)
CONTINUE

CONTINUE
(' ','ENTER THE NUMBER OF COMPONENTS (AS AN INTEGER)')

FORMAT
FORMAT
FORMAT
FORMAT

FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
RETURN
END

(1X,'ENTER THE SYSTEM PRESSURE IN ATMOSPHERES')

(1X,'ENTER AN INITIAL GUESS FOR THE SYSTEM TEMPERATURE')

(1X,'ENTER THE NAME OF COMPONENT #',Il,'

'/1X,'CARBON DIOXIDE
'/1X,'ETHYLENE
'/1X,'BIPHENYL

(' '.'INPUT K('.Il.'.'.11.')')

(X.A4)

(11)

(4C10.4)

(A4)

(4C10.4)
(3610.4)
(Ah/AA/AA/AA)

- 002
- CZHh
- BIPH

ETHANE

NAPHTHALENE
PHENANTHRENE

- CZH6
- NAPT
- PHAN

')

WWW

* SUBROUTINE FIXXY
******************************************************************
* THIS SUBROUTINE RETURNS VALUES FOR MOLE FRACTIONS WEIGHTED BY *

* THE INITIAL GUESSES
******************************************************************

E E E

*

I
NC
X(I)
Y(I)

* XSUM

*

YSUM

DO LOOP INDEX
THE NUMBER OF COMPONENTS
THE MOLE FRACTION OF COMPONENT I IN THE LIQUID
THE MOLE FRACTION OF COMPONENT I IN THE VAPOR
SUM OF THE X(I) VALUES -

SUM OF THE Y(I) VALUES
****************************************************************

SUBROUTINE FIXXY (NC,DX,DY,X,Y)
DIMENSION X(3),Y(3)
DOUBLE PRECISION DX(3),DY(3)
XSUM - 0.0
YSUM - 0.0
D0 100 I - 1,NC

XSUM - XSUM + X(I)

YSUM - YSUM + Y(I)

*

*

139363639363!-

(I(]()()(,()(,()()()C1C)C)C)C)C)C)C)C)C)C)C)C)C)C)

100

200
77

Q‘Q'Q‘Q'R‘Q‘Q'Q‘Q‘

106

CONTINUE
IF (XSUM.EQ.0.0) THEN
WRITE (6,77)
STOP
ENDIF
IF (YSUM.EQ.0.0) THEN
WRITE (6,77)
STOP
ENDIF
DO 200 I - 1,NC
X(I) - X(I)/XSUM
DX(I) - DBLE(X(I))
Y(I) - Y(I)/YSUM
DY(I) - DBLE(Y(I))
CONTINUE
FORMAT (X,'ERROR ERROR ERROR ERROR ERROR ERROR ERROR ERROR
',/X,'ERROR ERROR ERROR ERROR ERROR ERROR ERROR ERROR
',/X,'ERROR ERROR ERROR ERROR ERROR ERROR ERROR ERROR
',/X,'ERROR ERROR
',/X,'ERROR I AM AFRAID YOU ARE CLAIMINC ERROR
',/X,'ERROR ALL MOLE FRACTIONS ARE ZERO! ERROR
',/X,'ERROR ERROR
',/X,'ERROR ERROR ERROR ERROR ERROR ERROR ERROR ERROR
',/X,'ERROR ERROR ERROR ERROR ERROR ERROR ERROR ERROR
',/X,'ERROR ERROR ERROR ERROR ERROR ERROR ERROR ERROR')
RETURN
END
******************************************************************
* SUBROUTINE SFUC *
******************************************************************
* THIS ASSUMES COMPONENT 1 TO BE GAS AND 2 AND 3 SOLIDS. *
******************************************************************
* VARIABLES *

* ANT(I,J) Jth ANTOINE COEFFICIENT FOR COMPONENT I *
* DANTA A COEFFICIENT FOR THE ANTOINE EQUATION FOR THE SOLID *
* DANTB B COEFFICIENT FOR THE ANTOINE EQUATION FOR THE SOLID *
* DANTC C COEFFICIENT FOR THE ANTOINE EQUATION FOR THE SOLID *
* DEN SYSTEM DENSITY IN MOLES/CC *
* DFG(I) FUGACITY OF COMPONENT I *
* DP SYSTEM PRESSURE IN BARS *
* DPSAT(I) SATURATION PRESSURE (IN UNITS OF BAR) OF COMPONENT I *
* AT SYSTEM TEMPERATURE *
* DPSATPA SATURATION PRESSURE (IN UNITS OF Pa) OF SOLID AT *
* SYSTEM TEMPERATURE *
* DR GAS CONSTANT (IN CC-BAR/GMOLE-K) *
* DT DOUBLE PRECISION T *
* DVSOL(I) DOUBLE PRECISION VSOL(I) *
* NC NUMBER OF COMPONENTS IN THE SYSTEM *
* T SYSTEM TEMPERATURE IN KELVIN *
* VSOL(I) VOLUME OF SOLID COMPONENT I IN CC/GMOLE *

******************************************************************

107

SUBROUTINE SFUG (ANT,DFG,NC,DP,T,VSOL)
REAL ANT(3,3),VSOL(3)
DOUBLE PRECISION DANTA,DANTB,DANTC,DFG(3),DPSAT(3),DPSATPA,DP
DOUBLE PRECISION DR,DT,DVSOL(3)
DR - DBLE(83.1439)
DT - DBLE(T)
DO 400 I - 2,NC
DANTA - DBLE(ANT(I,1))
DANTB - DBLE(ANT(I,2))
DANTC - DBLE(ANT(I,3))
DPSATPA - 10.D0**(DANTA-DANTB/(DT+DANTC))
DPSAT(I) - DPSATPA/1.D05
C WWWW”
C * CALCULATE SOLID FUGACITY *
C HWWWM
DVSOL(I) - DBLE(VSOL(I))
DFG(I) - DPSAT(I)*DEXP(DVSOL(I)*(DP-DPSAT(I))/DR/DT)
400 CONTINUE

DBSTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2

DBTERM RATIO DB(I)/DBM, USED IN CALCULATING FUGACITY
COEFFICIENT OF COMPONENT I

DEL USED IN CALCULATING FUGACITY COEFFICIENTS

DELY(I) CHANGE IN VALUE OF DY(I) FROM LAST ITERATION

DFG(I) FUGACITY OF COMPONENT I

DFOMEG FUNCTION OF OMEGA USED IN CALCULATING DA(I) VALUES

DK(I,J) DOUBLE PRECISION K(I,J)

DNEWY(I) NEXT GUESS FOR DY(I)

RETURN
END
c ******************************************************************
C * SUBROUTINE VEOS USING ORIGINAL PENG-ROBINSON EOS *
c ******************************************************************
C * A0 ------ THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC *
C * EQUATION TO BE SOLVED *
C * A1 ------ THE FIRST ORDER TERM OF THE NORMALIZED CUBIC *
C * EQUATION TO BE SOLVED *
C * A2 ------ THE SECOND ORDER TERM OF THE NORMALIZED CUBIC *
C * EQUATION TO BE SOLVED *
C * ASTAR SINGLE PRECISION DASTAR *
C * BSTAR SINGLE PRECISION DBSTAR *
C * C1 IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC *
C * C2 IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC *
C * C3 IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC *
C * C(I) VOLUME TRANSLATION FOR COMPONENT I - NOT USED IN *
C * THIS SUBROUTINE *
C * DA(I) PENG-ROBINSON a FOR PURE COMPONENT I *
C * DAM E OF THE MIXTURE *
C * DASTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION *
C * TO SOLVE FOR 2 *
C * DB(I) PENG-ROBINSON b FOR PURE COMPONENT I *
C * DBM b OF THE MIXTURE *
(2 * *
<3 * *
(2 * *
C * *
C at 9:
C: E E
C: * *
C: E *
C * *
C * 9c

108

C E DOM(I) DOUBLE PRECISION OM(I) E
C E DP TOTAL SYSTEM PRESSURE (BAR) *
C E DR DOUBLE PRECISION R E
C E DRLT FIRST LOGARITHMIC TERM USED IN CALCULATING E
C E FUGACITY COEFFICIENTS E
C E DRLT2 SECOND LOGARITHMIC TERM USED IN CALCULATING E
C E FUGACITY COEFFICIENTS E
C E DT DOUBLE PRECISION T *
C E DTC(I) DOUBLE PRECISION TC(I) E
C E DTR DOUBLE PRECISION TR E
C E DY(I) VAPOR PHASE MOLE FRACTION OF COMPONENT I E
C E Dz DOUBLE PRECISION z E
C E I COMPONENT SUBSCRIPT E
C E ICNT ITERATION LOOP COUNTER E
C E J COMPONENT SUBSCRIPT E
C E K(I,J) INTERACTION PARAMETER FOR THE I,J COMPONENT PAIR E
C E NC TOTAL NUMBER OF COMPONENTS E
C E OM(I) PITZER ACENTRIC FACTOR E
C *. PC(I) CRITICAL PRESSURE OF COMPONENT I E
C E PHI(I) FUGACITY COEFFICIENT OF COMPONENT I IN THE MIXTURE E
c: E R GAS CONSTANT (CC-BAR/MOL-X) E
<: E R1 REAL PART OF THE lST ROOT OF THE SOLVED CUBIC E
c: E R2 REAL PART OF THE 2ND ROOT OF THE SOLVED CUBIC E
<3 E R3 REAL PART OF THE 3RD ROOT OF THE SOLVED CUBIC E
<3 E T SYSTEM TEMPERATURE (KELVIN) E
<3 E TC(I) CRITICAL TEMPERATURE OF COMPONENT I (KELVIN) E
<3 E TR REDUCED TEMPERATURE E
<3 E v VAPOR PHASE MOLAR VOLUME (CC/MOL) OF MIXTURE AT E
<3 E SYSTEM P AND T E
<3 E z VAPOR PHASE COMPRESSIBILITY OF MIXTURE E
C H“W*****W*m****‘k************************************

SUBROUTINE VEOS (C,DFG,K,NC,OM,DP,PC,DPHI,T,TC,V,DY,DZ)
REAL C(3),K(3,3),OM(3),PC(3),TC(3)
DOUBLE PRECISION DA(3),DAM,DASTAR,DB(3),DBM,DBSTAR,DBTERM,DEL
DOUBLE PRECISION DELY(3),DFG(3),DFOMEG,DK(3,3),DNEWY(3),DOM(3)
DOUBLE PRECISION DP,DPC(3),DPHI(3),DR,DRLNPHI,DRLT,DRLT2,DT
DOUBLE PRECISION DTC(3),DTR,DY(3),DZ
R - 83.1439
DR - DBLE(R)
DT - DBLE(T)
DO 20 J - 1,NC
DOM(J) - DBLE(OM(J))
DPC(J) - DBLE(PC(J))
DTC(J) - DBLE(TC(J))
DTR-DT/DTC(J)
DFOMEG-3.7464D-14-1.54226D0*DOM(J)-2.6992D-1*DOM(J)**2.D0
DA(J) - 4.5724D-1*(DR*DTC(J)*(1.D0 + DFOMEG*(1.DO -
as. DSQRT(DTR) ) ) )EE2 .DO/DPC(J)
DB(J) - 7.78D-2*DR*DTC(J)/DPC(J)
12¢) CONTINUE
C WWW
C * BEGINNING OF LOOP FOR COMPOSITION E
C WWWMW*M*

109

24 DAMEO
DBM-O
Do 30 I - 1,NC
DBM - DBM + DY(I)EDB(I)
DO 25 J - 1,NC
DK(I,J) - DBLE(K(I,J))
DAM-DAM+DY(I)*DY(J)*DSQRT(DA(I)*DA(J))*(1.DO-DK(I,J))
25 CONTINUE
3O CONTINUE
CMM
C E SOLVE CUBIC Eos E
CMM
DASTAR - DAMEDP/(DREDT)EE2
ASTAR - SNGL(DASTAR)
DBSTAR - DBMEDP/DR/DT
BSTAR - SNGL(DBSTAR)
A2 - BSTAR-1.
A1 - ASTAR-BSTARE(2. + 3.EBSTAR)
Ao - BSTARE(BSTAREE2 + BSTAR - ASTAR)
CALL CUBIC(A2,A1,AO,R1,R2,R3,C1,C2,C3,IFLAG)

c MWWWWEEWEE
(3 * IFLAG - 1 MEANS ONE REAL + TWO COMPLEX *
(I * - 2 ALL REAL, AT LEAST TWO SAME *
(I * - 3 THREE DISTINCT REAL ROOTS *
c mmmmmmm
IF (IFLAG.EQ.1)THEN
Z - R1
ELSE IF (IFLAG.EQ.2) THEN
Z - R1
IF (Z.LT.R2) Z-R2
ELSE
Z - R1

IF (2.LT.R2) z-R2
IF (z.LT.R3) z-R3
ENDIF
Dz - DBLE(Z)
V - ZEDREDT/DP
C “WNWWW*****
C * CALCULATE VAPOR PHASE FUGACITIES E
C “*HWWWH
DRLT - DLOG((2.DOEDz + DBSTARE(2 D0 + DSQRT(B DO)))/(2 DOEDz +
& DBSTARE(2.DO - DSQRT(B.D0))))
DRLT2 - DLOG(Dz - DBSTAR)
DO 700 L - 1,NC
DBTERM - DB(L)/DBM
DEL - o.DO
DO 600 LL - 1,NC
DEL - DEL + 2.D0EDY(LL)EDSQRT(DA(L)EDA(LL))E(1.DO -

a. DR(L, LL) )/DAM
600 CONTINUE
DRLNPHI - DBTERME(Dz - 1.D0) - DRLT2 + DASTARE(DBTERM -
6E DEL)EDRLT/DBSTAR/DSQRT(8.DO)

DPHI(L) - DEXP(DRLNPHI)

()(JC)(DC)C)C)(DC)C)()()()()C)C)C)C)C)<)C>(It)cacacuc:cucacacaczcacucucacacacu

700

750

800

110

DNEWY(L) - DFG(L)/DPHI(L)/DP
DELY(L) - DABS((DNEWY(L)-DY(L))/(DNEWY(L)+DY(L)))
DY(L) - (DNEWY(L)+3*DY(L))/4
CONTINUE
DY(I) - 1.00
DO 750 I - 2,NC
DY(I) - DY(I) - DY(I)
CONTINUE
DO 800 L - 2,NC
IF (DELY(L).GT.1D-04) GOTO 24

CONTINUE
RETURN
END
WWWflWWWWW
* SUBROUTINE LEOS USING ORIGINAL PENG-ROBINSON EOS *
WW*“WWWWW
A0 ------ THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED
A1 ------ THE FIRST ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED
A2 ------ THE SECOND ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED
ASTAR SINGLE PRECISION DASTAR
BSTAR SINGLE PRECISION DBSTAR
Cl IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC
C2 IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC
C3 IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC
C(I) VOLUME TRANSLATION FOR COMPONENT I - NOT USED IN
THIS SUBROUTINE
DA(I) PENG-ROBINSON 3 FOR PURE COMPONENT I
DAM 3 OF THE MIXTURE
DASTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2
DB(I) PENG-ROBINSON b FOR PURE COMPONENT I
DBM b OF THE MIXTURE

DBSTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2

DBTERM RATIO DB(I)/DBM, USED IN CALCULATING FUGACITY
COEFFICIENT OF COMPONENT I

DEL USED IN CALCULATING FUGACITY COEFFICIENTS

DFG(I) FUGACITY OF COMPONENT I

DFOMEG FUNCTION OF OMEGA USED IN CALCULATING DA(I) VALUES

DK(I,J) DOUBLE PRECISION K(I,J)

DOM(I) DOUBLE PRECISION OM(I)

DP TOTAL SYSTEM PRESSURE (BAR)

DR DOUBLE PRECISION R

DRLT FIRST LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

DRLTZ SECOND LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

DT DOUBLE PRECISION T

*fi-fifl-i’l-l-M-l-Il-M'M-M-M-M-X-M-M-M-M-M-M-M-M-fl-M-fl-X-l-l-M-M-X-fl'fl-M-
*1-fifl-X-X-M-M-M-fi-M-X-fl-M-M-M-M-M'M-M-*X'X-M-X-fl-l-X-M-M-M-M-X-M-M-M-

DTC(I) DOUBLE PRECISION TC(I)

OOOOOOOOOOOOOOOOOOOOOO

*fiI-X-i-fl-l-fi-fi-fi-X-fl-I-X-fl-fl-fl-fl-X-X-fl-

DTR
DX(I)
DZ

ICNT
K(I,J)
NC
OM(I)
PC(I)
PHI(I)
R1

R3

TC(I)

“E

Z

111

DOUBLE PRECISION TR

LIQUID PHASE MOLE FRACTION OF COMPONENT I

DOUBLE PRECISION Z

COMPONENT SUBSCRIPT

ITERATION LOOP COUNTER

COMPONENT SUBSCRIPT

INTERACTION PARAMETER FOR THE I,J COMPONENT PAIR
TOTAL NUMBER OF COMPONENTS

PITZER ACENTRIC FACTOR

CRITICAL PRESSURE OF COMPONENT I

FUGACITY COEFFICIENT OF COMPONENT I IN THE MIXTURE
GAS CONSTANT (CC-BAR/MOL-K)

REAL PART OF THE IST ROOT OF THE SOLVED CUBIC
REAL PART OF THE 2ND ROOT OF THE SOLVED CUBIC
REAL PART OF THE 3RD ROOT OF THE SOLVED CUBIC
SYSTEM TEMPERATURE (KELVIN)

CRITICAL TEMPERATURE OF COMPONENT I (KELVIN)
REDUCED TEMPERATURE

LIQUID PHASE MOLAR VOLUME (CC/MOL) OF MIXTURE AT
SYSTEM P AND T

LIQUID PHASE COMPRESSIBILITY OF MIXTURE

l-X-X-X-X-fl-X-X-X-fi-fi-X-X-X-fl-X-X-X-X-fi-X-

******************************************************************
SUBROUTINE LEOS (C,DFG,K,NC,OM,DP,PC,DPHI,T,TC,V,DX,DZ)
REAL C(3),K(3,3),OM(3),PC(3),TC(3)

&

DOUBLE PRECISION DA(3),DAM,DASTAR,DB(3),DBM,DBSTAR,DBTERM,DEL

DOUBLE PRECISION DFG(3),DFOMEG,DK(3,3),DOM(3),DP,DPC(3),DPHI(3)

DOUBLE PRECISION DR,DRLNPHI,DRLT,DRLT2,DT,DTC(3),DTR,DX(3),DZ

R - 83.1439

DR - DBLE(R)

DT - DBLE(T)

DO 20 J - 1,NC
DOM(J) - DBLE(OM(J))
DPC(J) - DBLE(PC(J))
DTC(J) - DBLE(TC(J))
DTR-DT/DTC(J)
DFOMEG-3.7464D-14-1.54226DO*DOM(J)-2.6992D-1*DOM(J)**2.D0
DA(J) - 4.S724D-1*(DR*DTC(J)*(1.DO + DFOMEG*(1.DO -

DSQRT(DTR))))**2.DO/DPC(J)

DB(J) - 7.78D-2*DR*DTC(J)/DPC(J)
CONTINUE
c *************************************

C * BEGINNING OF LOOP FOR COMPOSITION *
c *************************************

DAM-O
DBM-0

DO 30 I - 1,NC

DBM - DBM + DX(I)*DB(I)
DO 25 J - 1,NC
DK(I,J) - DBLE(K(I,J))
DAM-DAM+DX(I)*DX(J)*DSQRT(DA(I)*DA(J))*(1.DO-DK(I,J))
CONTINUE
CONTINUE

CW

112

C * SOLVE CUBIC EOS *
*******************

C

00000

DASTAR - DAM*DP/(DR*DT)**2
ASTAR - SNGL(DASTAR)

DBSTAR - DBM*DP/DR/DT

BSTAR - SNGL(DBSTAR)

A2 - BSTAR-1.

A1 - ASTAR-BSTAR*(2. + 3.*BSTAR)

A0 - BSTAR*(BSTAR**2 + BSTAR - ASTAR)

CALL CUBIC(A2,A1,AO,R1,R2,R3,C1,C2,C3,IFLAG)

WWW*HM***W

* IFLAG - 1 MEANS ONE REAL + TWO COMPLEX *
* - 2 ALL REAL, AT LEAST TWO SAME *
* - 3 THREE DISTINCT REAL ROOTS *

WWW**MW

IF (IFLAG.EQ.1)THEN
z - R1
ELSE IF (IFLAG.EQ.2) THEN
z - R1
IF (Z.CT.R2) Z-R2
ELSE
z - R1
IF (Z.GT.R2) Z-R2
IF (Z.GT.R3) Z-R3
ENDIF
Dz - DBLE(Z)
v - Z*DR*DT/DP

C WIPWW

C * CALCULATE LIQUID PHASE FUGACITIES *
c *************************************

000000

600

700

&

DRLT - DLOG((2.DO*DZ + DBSTAR*(2.DO + DSQRT(8.DO)))/(2.DO*DZ +
DBSTAR*(2.DO - DSQRT(8.DO))))
DRLTZ - DLOG(DZ - DBSTAR)
Do 700 L - 1,Nc
DBTERM - DB(L)/DBM
DEL - o.Do
Do 600 LL - 1,NC
DEL - DEL + 2.D0*DX(LL)*DSQRT(DA(L)*DA(LL))*(1.D0 -
DK(L,LL))/DAM
CONTINUE
DRLNPHI - DBTERM*(DZ - 1.DO) - DRLTZ + DASTAR*(DBTERM -

DEL)*DRLT/DBSTAR/DSQRT(8.DO)
DPHI(L) - DEXP(DRLNPHI)
CONTINUE
RETURN
END

WWM*WH*WNWWWHN****M**

* SUBROUTINE CUBIC *
******************************************************************
* THIS SUBROUTINE FINDS THE ROOTS OF A CUBIC EQUATION OF THE *
* FORM X**3 + A2*X**2 + A1*X + A0 - O ANALYTICALLY. *
******************************************************************

000000000000000000000000000000000000000000000

113

* Ao ------- THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC
* EQUATION

* A1 ------- THE FIRST ORDER TERM OF THE NORMALIZED CUBIC

* EQUATION

* A2 ------- THE SECOND ORDER TERM OF THE NORMALIZED CUBIC

* EQUATION

* c1 ------- THE COMPLEX ARGUMENT OF ROOT #1 OF THE EQUATION
* C2 ------- THE COMPLEX ARGUMENT OF ROOT #2 OF THE EQUATION
* C3 ------- THE COMPLEX ARGUMENT OF ROOT #3 OF THE EQUATION
* CCHECR --- THE SAME As ”CHECK” BUT CONVERTED TO COMPLEX

* NUMBER FORMAT

* CHECK ---- Q**3 + R**2, USED TO CHECK FOR THE CASE OF THE
* SOLUTION AND IN FINDING THE ROOTS OF THE EQUATION,
* DOUBLE PRECISION

* DAO ------ 'AO' CONVERTED TO DOUBLE PRECISION

* DA1 ------ “A1” CONVERTED TO DOUBLE PRECISION

* DA2 ------ "A2” CONVERTED TO DOUBLE PRECISION

* ESI ------ AN INTERMEDIATE CALCULATION TO USED IN THE

* CALCULATION OF "81"

* E32 ------ AN INTERMEDIATE CALCULATION TO USED IN THE

* CALCULATION OF "82"

* IFLAG ---- A FLAG TO INDICATE THE CASE OF THE SOLUTION OF THE
* EQUATION: -1 ONE REAL + Two COMPLEX ROOTS,

* -2 ALL REAL ROOTS, AT LEAST Two THE SAME
* -3 THREE DISTINCT REAL ROOTS

* P1 ------- ' AN INTERMEDIATE SUM USED IN THE CALCULATION OF
* 'SSI'

* P2 ------- AN INTERMEDIATE SUM USED IN THE CALCULATION OF
* ”ssz-

* Q -------- AN INTERMEDIATE SUM USED IN CALCULATING “CHECK"
* R -------- AN INTERMEDIATE SUM USED IN CALCULATING "CHECK“
* R1 ------- THE REAL ARGUMENT OF ROOT #1 OF THE EQUATION

* R2 ------- THE REAL ARGUMENT OF ROOT #2 OF THE EQUATION

* R3 ------- THE REAL ARGUMENT OF ROOT #3 OF THE EQUATION

* RECK ----- THE SAME AS ”CHECK", BUT SINGLE PRECISION REAL
* S1 ------- AN INTERMEDIATE VALUE USED TO FIND THE ROOTS OF
* THE EQUATION, COMPLEX NUMBER

* S2 ------- AN INTERMEDIATE VALUE USED TO FIND THE ROOTS OF
* THE EQUATION, COMPLEX NUMBER

* SSl ------ THE SAME As 51 BUT DOUBLE PRECISION REAL

* ssz ------ THE SAME AS 32 BUT DOUBLE PRECISION REAL

* 21 ------- ROOT #1 OF THE EQUATION, COMPLEX NUMBER

* 22 ------- ROOT #2 OF THE EQUATION, COMPLEX NUMBER

* 23 ------- ROOT #3 OF THE EQUATION, COMPLEX NUMBER

361-1-391-36361-3!-30363636393!-$31-363(-*fl-fl-X-fl-fi-fl-fi-X-fl-X-X-fi-fi-X-fl-X-X-fix-X-N-d-X-SI-

WWW“**MWW“

SUBROUTINE CUBIC(A2,A1,AO,R1,R2,R3,C1,C2,C3,IFLAG)
DOUBLE PRECISION CHECK,DAO,DA1,DA2,P1,P2,Q,R,SSl,SSZ
COMPLEX ESI,E32,SI,S2,21,22.23,CCHECR

DAO - DBLE(AO)

DA1 - DBLE(AI)

DA2 - DBLE(A2)

Q - DA1/3.D00 - DA2*DA2/9.DOO

R - (DA1*DA2 - 3.DOO*DAO)/6.DOO - (DA2/3.DOO)**3

(ICICICIC)

114

CHECK - Q**3 + R*R
IF (CHECK.GT.1.OE-10) THEN
IFLAC - 1
P1 - R + DSQRT(CHECK)
P2 - R - DSQRT(CHECK)
IF (P1.LT.O.O) THEN
SSI - -DEXP((DLOG(-1.DOO*P1))/3.DOO)
ELSE
SSI - DEXP((DLOC(P1))/3.DOO)
ENDIF
IF (P2.LT.O.O) THEN
ssz - -DEXP((DLOG(-1.DOO*P2))/3.DOO)
ELSE
ssz - DEXP((DLOG(P2))/3.DOO)
ENDIF
R1 - $81 + 332 - DA2/3.DOO
R2 -(SSl + SS2) - DA2/3.D00
R3 R2
CI 0.0
C2 (SQRT(3.))*(SSI - ssz)/2.DOO
C3 - -C2
ELSE IF (CHECK.LT.O.O) THEN
IFLAC - 3
RR - 1.*R
RECK - 1.*CHECK
CCHECK - CMPLX(RECK,O.O)
ESl - CLOG(RR + CSQRT(CCHECK))/3.
E82 - CLOG(RR - CSQRT(CCHECK))/3.
SI - CEXP(ES1)
$2 - CEXP(E52)

21 - ($1 + 82) - A2/3
22 - -(Sl + SZ)/2 - A2/3 + (CMPLX(0.0,3**.5))*(SI - $2)/2
23 - ~(Sl + $2)/2 - A2/3 - (CMPLX(0.0,3**.S))*(SI - 82)/2
R1 - REAL(ZI)
R2 - REAL(ZZ)
R3 - REAL(Z3)
C1 - 0.0
C2 - Cl
C3 - Cl
ELSE

WWM******MMWWMW*W

* IF THE ROOTS OF THE EQUATION ARE VERY, VERY SMALL AND VERY, *
* VERY CLOSE TOGETHER, THIS SUBROUTINE MAY ERRONEOUSLY REPORT *

* THAT THE EQUATION HAS ONLY ONE ROOT NEAR ZERO *
****************************************************************
IFLAC - 2

IF (R.LT.O.O) THEN
SSI - -DEXP((DLOG(-1.DOO*R))/3.DOO)
ELSE IF (R.EQ.O.O) THEN
SSI - O.O
ELSE
SSI - DEXP((DLOG(R))/3.D00)
ENDIF

115

332 - SS1
R1 - SSI + $52 - DA2/3.DOO
R2 - -(SSl + ssz)/2 - DA2/3.DOO
R3 - R2
C1 - 0.0
C2 - C1
C3 - C2
ENDIF
RETURN

END

The following two subroutines were substituted for the

corresponding original Peng-Robinson subroutines when the

translated Peng-Robinson equation was used.

000000000000000000000000000000000000

*W“MH**H*H*W***WWWW****

* SUBROUTINE VEOS USING TRANSLATED PENG-ROBINSON EOS
******************************************************************

A0 ------ THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC

36$fl-3i-3I-l-fl-fl-fi-fl-X-X-N-N-$**fl-*$**fl-$$$fl-*$X-$**

C3
C(I)
DA(I)
DAM
DASTAR

DB(I)
DBM
DBSTAR

DBTERM

DEL
DELY(I
DFG(I)
DFOMEG
DX(I,J
DNEWY(
DOM(I)
DP

DR
DRLT

)

)
1)

EQUATION TO BE SOLVED

THE FIRST ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED

THE SECOND ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED

SINGLE PRECISION DASTAR

SINGLE PRECISION DBSTAR

IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC
IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC
IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC
VOLUME TRANSLATION FOR COMPONENT I

PENG-ROBINSON 8 FOR PURE COMPONENT I

a OF THE MIXTURE

INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2

PENG-ROBINSON b FOR PURE COMPONENT I

b OF THE MIXTURE

INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2

RATIO DB(I)/DBM, USED IN CALCULATING FUGACITY
COEFFICIENT OF COMPONENT I

USED IN CALCULATING FUGACITY COEFFICIENTS

CHANGE IN VALUE OF DY(I) FROM LAST ITERATION
FUGACITY OF COMPONENT I

FUNCTION OF OMEGA USED IN CALCULATING DA(I) VALUES
DOUBLE PRECISION K(I,J)

NEXT GUESS FOR DY(I)

DOUBLE PRECISION OM(I)

TOTAL SYSTEM PRESSURE (BAR)

DOUBLE PRECISION R

FIRST LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

*

3(-361-1-361-36391-1-X-36-X-X'X-i-fl-X-X-X-X-fl-X-fi-X-X-X-N-fii-X-X'X-

C)C)(ICICICacucucacacucacucaricatucuczcucucacucacacacu

12()

IZ¢L

a-a-a-a-x-at-x-x-a-a-a-aFa-x-x-x-a-a-x-a-x-M-x-x-x-ae

DRLTZ

DT
DTC(I)
DTR
DY(I)
DZ

I
ICNT
J
K(I,J)
NC
OM(I)
PC(I)
PHI(I)
R

R1

R2

R3

T
TC(I)
TR

TZ

V

Z

116

SECOND LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

DOUBLE PRECISION T

DOUBLE PRECISION TC(I)

DOUBLE PRECISION TR

VAPOR PHASE MOLE FRACTION OF COMPONENT I

DOUBLE PRECISION Z

COMPONENT SUBSCRIPT

ITERATION LOOP COUNTER

COMPONENT SUBSCRIPT

INTERACTION PARAMETER FOR THE I,J COMPONENT PAIR
TOTAL NUMBER OF COMPONENTS

PITZER ACENTRIC FACTOR

CRITICAL PRESSURE OF COMPONENT I

FUGACITY COEFFICIENT OF COMPONENT I IN THE MIXTURE
GAS CONSTANT (CC-BAR/MOL-K)

REAL PART OF THE IST ROOT OF THE SOLVED CUBIC
REAL PART OF THE 2ND ROOT OF THE SOLVED CUBIC
REAL PART OF THE 3RD ROOT OF THE SOLVED CUBIC
SYSTEM TEMPERATURE (KELVIN)

CRITICAL TEMPERATURE OF COMPONENT I (KELVIN)
REDUCED TEMPERATURE

TRUE VAPOR PHASE COMPRESSIBILITY OF MIXTURE
VAPOR PHASE MOLAR VOLUME (CC/MOL) OF MIXTURE AT
SYSTEM P AND T

VAPOR PHASE COMPRESSIBILITY OF MIXTURE

x-x-M-a-x-x-x-aeat-x-x-N-a-x-x-x-x-M-x-x-x-x-x-x-x-u-

*“WW*W*WWWW**WWW**
SUBROUTINE VEOS (C,DFG,K,NC,OM,DP,PC,DPHI,T,TC,V,DY,TZ)
REAL C(3),K(3,3),OM(3),PC(3),TC(3)
DOUBLE PRECISION DA(3),DAM,DASTAR,DB(3),DBM,DBSTAR,DBTERM,DC(3)
DOUBLE PRECISION DCM,DEL,DELY(3),DFG(3),DFOMEG,DK(3,3),DNEWY(3)
DOUBLE PRECISION DOM(3),DP,DPC(3),DPHI(3),DR,DRLNPHI,DRLT,DRLT2
DOUBLE PRECISION DT,DTC(3),DTR,DY(3),DZ,TZ
R - 83.1439
DR - DBLE(R)
DT - DBLE(T)
DO 20 J - 1,NC

DC(J) - DBLE(C(J))

DOM(J) - DBLE(OM(J))

DPC(J) - DBLE(PC(J))

DTC(J) - DBLE(TC(J))

DTR-DT/DTC(J)

&:

DFOMEG - 3.7464D-1 + 1.54226D0*DOM(J) - 2.6992D-1*DOM(J)**2

DA(J) - 4.5724D-1*(DR*DTC(J)*(1.DO + DFOMEG*(1.D0 -

DSQRT(DTR))))**2.DO/DPC(J)

DB(J) - 7.78D-2*DR*DTC(J)/DPC(J)
CONTINUE

C Warmmmmwum

C * BEGINNING OF LOOP FOR COMPOSITION *

C ***mm*w*mm*m*****m

DAM - 0.0DO

DBM - 0.0D0

DCM - 0.0D0

25
30

000

3"
*

00000

117

D0 30 I - 1,NC

DBM - DBM + DY(I)*DB(I)

DCM - DCM + DY(I)*DC(I)

DO 25 J - 1,NC
DK(I,J) - DBLE(K(I,J))
DAM-DAM+DY(I)*DY(J)*DSQRT(DA(I)*DA(J))*(1.DO-DK(I,J))
CONTINUE

CONTINUE

WW

* SOLVE CUBIC EOS *
*******************

DASTAR - DAM*DP/(DR*DT)**2

ASTAR - SNGL(DASTAR)

DBSTAR - DBM*DP/DR/DT

BSTAR - SNGL(DBSTAR)

A2 - BSTAR-1.

A1 - ASTAR-BSTAR*(2. + 3.*BSTAR)

A0 - BSTAR*(BSTAR**2 + BSTAR - ASTAR)

CALL CUBIC(A2,A1,AO,R1,R2,R3,C1,C2,C3,IFLAG)

***********************************************
* IFLAC - 1 MEANS ONE REAL + TWO COMPLEX *

- 2 ALL REAL, AT LEAST TWO SAME *
- 3 THREE DISTINCT REAL ROOTS *

WWW***WW

IF (IFLAG.EQ.1)THEN
2 - R1
ELSE IF (IFLAG.EQ.2) THEN
2 - R1
IF (2.LT.R2) 2-R2
ELSE
2 - R1
IF (2.LT.R2) z-R2
IF (2.LT.R3) z-R3
ENDIF
Dz - DBLE(Z)
T2 - D2 - DCM*DP/DR/DT
v - TZ*DR*DT/DP

C Wmmmmum

C: ** CALCULATE VAPOR PHASE FUGACITIES *
c: sva**********************************

£5()()

DRLT - DLOG((2.DO*DZ + DBSTAR*(2.DO + DSQRT(8.DO)))/(2.DO*DZ +
DBSTAR*(2.DO - DSQRT(8.DO))))
DRLT2 - DLOG(D2 - DBSTAR)
DO 700 L - 1,NC
DBTERM - DB(L)/DBM
DEL - O.Do
DO 600 LL - 1,NC
DEL - DEL + 2.D0*DY(LL)*DSQRT(DA(L)*DA(LL))*(1.DO -
DK(L,LL))/DAM
CONTINUE
DRLNPHI - DBTERM*(DZ - 1.D0) - DRLT2 + DASTAR*(DBTERM -
DEL)*DRLT/DBSTAR/DSQRT(8.DO) - DC(L)*DP/DR/DT
DPHI(L) - DEXP(DRLNPHI)

700

750

800

118

DNEWY(L) - DFG(L)/DPHI(L)/DP
DELY(L) - DABS((DNEWY(L)-DY(L))/(DNEWY(L)+DY(L)))
DY(L) - (DNEWY(L)+3*DY(L))/4
CONTINUE
DY(I) - 1.DO
DO 750 I - 2,NC
DY(I) - DY(l) - DY(I)
CONTINUE

DO 800 L - 2,NC
IF (DELY(L).GT.1D-04) GOTO 24

CONTINUE
RETURN
END
WW***NWWWWW
* SUBROUTINE LEOS USING TRANSLATED PENG-ROBINSON EOS *
W**MNHW*W*W*WWMW**
AO ------ THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED
A1 ------ THE FIRST ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED
A2 ------ THE SECOND ORDER TERM OF THE NORMALIZED CUBIC
EQUATION TO BE SOLVED
ASTAR SINGLE PRECISION DASTAR
BSTAR SINGLE PRECISION DBSTAR
C1 IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC
C2 IMAGINARY PART OF THE 1ST ROOT OF THE SOLVED CUBIC
C3 IMAGINARY PART OF THE IST ROOT OF THE SOLVED CUBIC
C(I) VOLUME TRANSLATION FOR COMPONENT I
DA(I) PENG-ROBINSON 3 FOR PURE COMPONENT I
DAM E OF THE MIXTURE
DASTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2
DB(I) PENG-ROBINSON b FOR PURE COMPONENT I
DBM b OF THE MIXTURE

DBSTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION
TO SOLVE FOR 2

DBTERM RATIO DB(I)/DBM, USED IN CALCULATING FUGACITY
COEFFICIENT OF COMPONENT I

DEL USED IN CALCULATING FUGACITY COEFFICIENTS

DFG(I) FUGACITY OF COMPONENT I

DFOMEG FUNCTION OF OMEGA USED IN CALCULATING DA(I) VALUES

DK(I,J) DOUBLE PRECISION K(I,J)

DNEWX(I) NEXT GUESS FOR DX(I)

DOM(I) DOUBLE PRECISION OM(I)

DP TOTAL SYSTEM PRESSURE (BAR)

DR DOUBLE PRECISION R

DRLT FIRST LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

DRLTZ SECOND LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

DT DOUBLE PRECISION T

# * x # # # * i * # $ $ s H * # S * * # » * * * # $ $ * $ $ $ * $ * H *

X'fil-fifl-X-X-fl-SI-l-I-fi-fl-fifl-fl-I'd-*fl-II-fl-fl-fl-X-l-fi-I-l-I-fifi-fl-I-M-fi-

DTC(I) DOUBLE PRECISION TC(I)

000000000000000000000000

fififl-fl-ififl-fi-fl-fl-fl-fifl-fl-fififl-fl-fifififififi

DTR
DX(I)
DZ

ICNT

K(I,J)
NC
NEWX(I)
OM(I)
PC(I)
PHI(I)
R

R1

R2

R3

T

TZ
TC(I)
TR

V

Z

119

DOUBLE PRECISION TR

LIQUID PHASE MOLE FRACTION OF COMPONENT I

DOUBLE PRECISION Z

COMPONENT SUBSCRIPT

ITERATION LOOP COUNTER

COMPONENT SUBSCRIPT

INTERACTION PARAMETER FOR THE I,J COMPONENT PAIR
TOTAL NUMBER OF COMPONENTS

NEXT GUESS FOR X(I)

PITZER ACENTRIC FACTOR

CRITICAL PRESSURE OF COMPONENT I

FUGACITY COEFFICIENT OF COMPONENT I IN THE MIXTURE
GAS CONSTANT (CC-BAR/MOL-K)

REAL PART OF THE IST ROOT OF THE SOLVED CUBIC
REAL PART OF THE 2ND ROOT OF THE SOLVED CUBIC
REAL PART OF THE 3RD ROOT OF THE SOLVED CUBIC
SYSTEM TEMPERATURE (KELVIN)

TRUE LIQUID PHASE COMPRESSIBILITY OF MIXTURE
CRITICAL TEMPERATURE OF COMPONENT I (KELVIN)
REDUCED TEMPERATURE

LIQUID PHASE MOLAR VOLUME (CC/MOL) OF MIXTURE AT
SYSTEM P AND T

PSEUDO LIQUID PHASE COMPRESSIBILITY OF MIXTURE

*fl-X-fi-X-X-X-fi-fl-fifl-fl-X-X-ififi-fifi-iffl-X-X-X-

******************************************************************
SUBROUTINE LEOS (C,DFG,K,NC,OM,DP,PC,DPHI,T,TC,V,DX,TZ)
REAL C(3),K(3,3),0M(3),PC(3),TC(3)

DOUBLE PRECISION DA(3),DAM,DASTAR,DB(3),DBM,DBSTAR,DBTERM,DC(3)
DOUBLE PRECISION DCM,DEL,DFG(3),DFOMEG,DK(3,3),DOM(3),DP,DPC(3)

&

DOUBLE PRECISION DPHI(3),DR,DRLNPHI,DRLT,DRLT2,DT,DTC(3),DTR

DOUBLE PRECISION DX(3),Dz,Tz

R - 83.1439

DR - DBLE(R)

DT - DBLE(T)

DO 20 J - 1,NC
DC(J) - DBLE(C(J))
DOM(J) - DBLE(OM(J))
DPC(J) - DBLE(PC(J))
DTC(J) - DBLE(TC(J))
DTR-DT/DTC(J)
DFOMEG - 3.7464D-1 + 1.54226D0*DOM(J) - 2.6992D-1*DOM(J)**2.
DA(J) - a.5724D-1*(DR*DTC(J)*(1.DO + DFOMEG*(1.DO -

DSQRT(DTR))))**2.DO/DPC(J)

DB(J) - 7.78D-2*DR*DTC(J)/DPC(J)
CONTINUE
c *************************************

C * BEGINNING OF LOOP FOR COMPOSITION *
c *************************************

DBM - DBM + DX(I)*DB(I)
DCM - DCM + DX(I)*DC(I)

25
30

000

'k
*

00000

120

D0 25 J - 1,NC
DK(I,J) - DBLE(K(I,J))
DAM-DAM+DX(I)*DX(J)*DSQRT(DA(I)*DA(J))*(1.D0-DK(I,J))
CONTINUE

CONTINUE

WWW

* SOLVE CUBIC EOS *
*******************

DASTAR - DAM*DP/(DR*DT)**2

ASTAR - SNGL(DASTAR)

DBSTAR - DBM*DP/DR/DT

BSTAR - SNGL(DBSTAR)

A2 - BSTAR-1.

A1 - ASTAR-BSTAR*(2. + 3.*BSTAR)

A0 - BSTAR*(BSTAR**2 + BSTAR - ASTAR)

CALL CUBIC(A2,Al,A0,R1,R2,R3,C1,CZ,C3,IFLAC)

***********************************************
* IFLAC - 1 MEANS ONE REAL + TWO COMPLEX *

- 2 ALL REAL, AT LEAST TWO SAME *
- 3 THREE DISTINCT REAL ROOTS *

WWW*W*HHW***W

IF (IFLAG.EQ.1)THEN
Z - R1
ELSE IF (IFLAG.EQ.2) THEN
Z - R1
IF (Z.GT.RZ) Z-R2
ELSE
Z - R1
IF (Z.GT.R2) Z-R2
IF (Z.GT.R3) Z-R3
ENDIF
DZ - DBLE(Z)
TZ - DZ - DCM*DP/DR/DT
V - TZ*DR*DT/DP

C mmmmmm*m******m

C * CALCULATE LIQUID PHASE FUGACITIES *
c *************************************

600

700

DRLT - DLOG((2.DO*DZ + DBSTAR*(2.DO + DSQRT(8.DO)))/(2.DO*DZ +
DBSTAR*(2.DO - DSQRT(8.DO))))
DRLT2 - DLOG(D2 - DBSTAR)
DO 700 L - 1,NC
DBTERM - DB(L)/DBM
DEL - O.Do
DO 600 LL - 1,NC
DEL - DEL + 2.D0*DX(LL)*DSQRT(DA(L)*DA(LL))*(1.DO -
DK(L,LL))/DAM
CONTINUE
DRLNPHI - DBTERM*(DZ - 1.DO) - DRLTz + DASTAR*(DBTERM -
DEL)*DRLT/DBSTAR/DSQRT(8.DO) - DC(L)*DP/DR/DT
DPHI(L) - DEXP(DRLNPHI)
CONTINUE
RETURN
END

121

The following page contains the data file PHASE5.DAT used

with these programs. The data for each substance are

organized according to the following grid:

Where:

1)

2)

3)
4)

5)

5)

7)

8)

9)

O is the acentric factor.

P T V are the pure component critical

0’ C’ C

pressure, temperature, and volume in bar, Kelvin,
and g/cc.

Tm is the pure component melting point in Kelvin.
6 is the solubility parameter in (cal/cc)%.

VL and VS are the molar volumes of the liquid and
solid respectively in cc/mol.

AHfus is the molar heat of fusion in cal/mol.

x and y are mole fractions in the liquid and vapor
phases.

c is the volume translation for the translated EOS
in cc/mol.

A, B, and C are the Antione coefficients for the

vapor pressure of the solid.

C02

0.
6.

1900
22

02H6
0

6.
682.

239
0

.0
.5898

.099
6
943

15.

02H4

0.

6

900.
15.

02H2

0.
5.
599.
16.

NAPT

O.
10.
4487.
12.

BIPH

0.
10.
4441.

15.
PHAN

0

9

4456

089
.6
9447
5368

190
329
9109
3481

302
07
7
808

372
56

277
6603

.4536
.777
.00

122

73.8 304.2 94.0
55.0 28.75 216.6
0.005 0.999 -1.6892
3103.39 -0.16
48.8 305.4 148.0
70.0 55.07 89.9
0.005 0.999 0.0
1511.42 -17.16
50.4 282.4 130.4
65.0 49.21 104.0
0.005 0.999 0.0
1347.01 -l8.15
61.4 308.3 112.7
42.18 77.? 192.4
0.005 0.999 0.0
1637.14 -19.77
40.5 748.4 413.0
123.0 111.93 353.5
0.995 0.001 4.1651
3270.8 -19.89
38.5 789.0 502.0
155.7677 132.8021 342.4
0.995 0.001 -9.2485
4993.366 22.922
27.43 869.25 554.0
167.667 152.8585 373.7
0.995 0.001 47.2597
.33 -31.597

12.9935 3922

References for data sources indexed by locatation in the above table

CO

000000000000000

2

W‘TM-d ~1'~<: MN

~r< «aha

P‘P‘

l) R. C. Reid, J. M. Prausnitz, B. E. Poling
The Properties of Gases & Liquids, 4ed.
McGraw-Hill, New York (1986)

2) S. Angus, B. Armstrong, K. M. Reuck
International Thermodynamic Tables of
the Fluid State - Vol. 3 Carbon Dioxide
Pergamon Press, New York (1976)

3) D. Ambrose, I.J. Lawrenseon, C. H. Sprake
J. Chem. Thermodynamics (1975) 7, 1173-76

4) A. F. M. Barton
Handbook of Solubility Parameters and
Other Cohesion Parameters
CRC Press, Boca Raton, FL (1983)

5) M. Grayson, D. Eckroth, eds.

Kirk-Othmer Encyclopedia of Chemical

00000000000000000000000000000000

02H2

*

l l 1
7 ? ? 6)
x y 0
F F
1 1 1 7)
? ? 1
x y 12*
3 3 8)
1 1 l
9 5 1 9)
x y 12*
9 9
8 8 8 10)
8 8 1
x y 8*
8 8
BASED ON LIQUID 11)
VOLUME DATA FROM
THIS SOURCE
12)
F)
7)

123

Technology

John Wiley & Sons, New York (1979)
R. C. Weast & M. J. Astle, eds.

CRC Handbook of Chemistry and Physics
63rd ed. 1982-1983

CRC Press, Boca Raton, FL

R. H Perry & C. H. Chilton, eds.
Chemical Engineers' Handbook 5th ed.
McGraw-Hill, New York (1973)

API Monograph Series ”Anthracene and
Phenanthrene", API Publication 708
Washington D.C. (January 1979)

J . Timme rmans

Physico-Chemical Constants of Pure
Organic Compounds

Elsevier, New York (1950)

J. M. Prausnitz

Molecular Thermodynamics of Fluid
Phase Equilibrium

Prentice-Hall, Englewood Cliffs, NJ
(1969)

E. J. Henley & J. D. Seader
Equilibrium-Stage Separation
Operations in Chemical Engineering
John Wiley & Sons, New York (1981)
DIPPR data base entries for this
component

False values used to fill the space
for this entry

Source of entry one of the above with
some unit conversions to get the value
entered in the table

APPENDIX E

ITERATION SCHEME FOR ISOTHERMAL SLV LINE DETERMINRTIONS IN

Notes: 1)

2)

3)

4)

5)

5)

TERNRRY SYSTEMS

The programs in Appendices D and F are used to make
these calculations.

x1 and y1 are the mole fractions of the solvent in
the liquid and vapor phases respectively.

yS is the mole fraction in the vapor phase of the
solute which is assumed to also form the single
pure solid phase.

yNS is the mole fraction in the vapor phase of the
solute which is assumed n9; to form a solid phase.
Since only one of the solutes forms a solid phase
in these calculations, the fugacity of the other
solute is not immediately fixed by a solid phase
fugacity, so fewer variable values are known at the
beginning of the calculations. For this reason,
the ratio Rv=yNS/yS is sought by iteration.

A slightly different method (relative to that given
in Appendix C) was used for updating the chosen
values of all xi. The main reason for this is that
the method given in this appendix seemed to be less
prone to crash if the initial guess for Rv is not

very good.

124

125

7) If cross parameters (kij for example) are used for

3)

the calculation of the d! and di’ values (steps 7

and 14), they must be entered during the execution

of the program.

This iteration scheme uses the following programs

from Appendices D and F:

Main
Program

INPUT

FIXXY

SFUG

VEOSZ

LEOS

This is the first program listed in
Appendix F. It follows the outline at the
beginning of this appendix (E) and calls
various subroutines to get initial and
intermediate data.

This subroutine reads initial variable
values. (Appendix D)

This subroutine returns values for mole
fractions weighted by the initial
guesses. (Appendix D)

This subroutine calculates the fugacities
of solid phases. (Appendix D)

This subroutine calculates vapor phase
fugacity coefficients. There are two
versions of this in Appendix F. The
first uses the original Peng-Robinson
EOS: the second uses the translated
Peng-Robinson EOS.

This subroutine calculates liquid phase

fugacity coefficients. There are two

CUBIC

126

versions of this in Appendix D. The
first uses the original Peng-Robinson
EOS: the second uses the translated
Peng-Robinson EOS.

This subroutine solves a cubic polynomial
for the three real or imaginary roots.
It is required in the subroutines VEOS

and LEOS. (Appendix D)

127

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'1. Fix T ‘ '7

2. Fix P

3. Guess ratio R = yNS/ys

(P‘Pfat)

4. folid=PsaceV1uud
i S 1 XP RT

5 y1 = 1 — ys(1+R,,')g

6 ym= YSRV ‘

7. Calculate all £p1

8- y; = s

’ ' ,, YS+Y5

11. Ayss 10“ ? “OJ

Yes

 

12.‘ f1=y1¢fp
13. Guess‘xi values ‘
14. Calculate all ()1

 

f1
15. x;=—

(PIP
16. Ax=l(x1—x1)/X1I
17. A=1—£x1‘

18. x1=(x1'+x1)/2
.. l-xl
19- Xyl'mxni

[gm Ax > 2.5x10“?] “3-
NO

 

 

 

 

 

 

 

 

IA I 210.3 ? Yes

new

 

NO

 

 

22. Output P, T, x, and y
23. Ne Xt P?

APPENDIX F

COMPUTER CODE FOR CALCULATING ISOTHERMAL SLV LINES IN
TERNARY SYSTEMS

Subroutines called in the programs of this apppendix but

not included in the appendix are listed in Appendix D.

c ******************************************************************
C * THIS PROGRAM CALCULATES THE COMPOSITION TRACE AT CONSTANT *
C * TEMPERATURE OF THE THREE-PHASE LINE (SLG) FOR A TERNARY SYSTEM *
C * WITH ONE LIGHT (I.E. GAS AT AMBIENT CONDITIONS) COMPONENT AND *
C * TWO HEAVY (I.E. SOLID AT AMBIENT CONDITIONS) COMPONENTS. *
C * COMPONENT 1 IS CHOSEN TO BE THE LIGHT COMPONENT. *
C * THE SUBSCRIPT OF THE HEAVY COMPONENT ASSUMED TO COMPRISE THE *
C * SOLID PHASE MUST BE SPECIFIED. *
C WHWfiHH*H***M*W**MWNWmW**
C

C W‘ki’m‘kfl*HH*******HH*WWWM****H*
C * ADELTAl ABSOLUTE VALUE OF DELTAl (IDELTAll) *
C * ADELTAZ ABSOLUTE VALUE OF DELTA2 (IDELTA2I) *
C * ANT(I,J) ANTOINE COEFFICIENTS OF COMPONENT I *
C * C(I) VOLUME TRANSLATION FOR COMPONENT I *
C * DELTAl NEW VALUE OF (FUGV - FUGL) *
C * DELTAZ OLD VALUE OF (FUGV - FUGL) *
C * DELTAT INCREMENTAL CHANGE TO T FOR THE NEXT ITERATION *
C * DHF(I) MOLAR HEAT OF FUSION OF PURE COMPONENT I AT ITS *
C * NORMAL MELTING POINT (CAL/G-MOLE) *
C * PC(I) FUGACITY OF PURE COMPONENT I IN THE GAS OR SCF *
C * PHASE *
C * FUGL LIQUID PHASE PARTIAL MOLAR FUGACITY OF COMPONENT l *
C * FUGV VAPOR PHASE PARTIAL MOLAR FUGACITY OF COMPONENT l *
C * I COMPONENT NUMBER *
C * INCR PRESSURE INCREMENT FOR THE NEXT LOOP (UNITS OF BAR) *
C * K(I,J) INTERACTION PARAMETER FOR COMPONENTS I AND J *
C * OMEGA(I) PITZER ACENTRIC FACTOR 0F COMPONENT I *
C * LV MOLAR VOLUME 0F LIQUID MIXTURE (CC/G-MOLE) *
C * NC NUMBER OF COMPONENTS IN THE SYSTEM *
C * P SYSTEM PRESSURE (UNITS OF BAR) *
C * P1 PRESSURE FOR THE FIRST LOOP (UNITS OF BAR) *
C * PC(I) THE CRITICAL PRESSURE OF PURE COMPONENT I IN UNITS *
C * OF BAR *
C * PHI(I) FUGACITY COEFFICIENT 0F COMPONENT I *
C * PTOP PRESSURE FOR THE LAST LOOP (UNITS OF BAR) *
C * PTOT SYSTEM PRESSURE (UNITS 0F ATM) *
C * SOLFG(I) GAS OR SCF PHASE FUGACITY OF COMPONENT I IN *

128

129

C * SOLUTION *
C * T SYSTEM TEMPERATURE IN UNITS OF KELVIN *
C * TC(I) THE CRITICAL TEMPERATURE OF PURE COMPONENT I IN *
C * UNITS OF KELVIN *
C * TDEGC SYSTEM TEMPERATURE IN DEGREES CELSIUS *
C * TM(I) NORMAL MELTING POINT OF PURE COMPONENT I (KELVIN) *
C * VC(I) THE CRITICAL VOLUME OF PURE COMPONENT I (CC/G-MOLE) *
C * VL(I) MOLAR VOLUME OF PURE LIQUID COMPONENT I (CC/G-MOLE) *
C * VS(I) MOLAR VOLUME OF PURE SOLID COMPONENT I (CC/G-MOLE) *
C * VV VOLUME OF VAPOR MIXTURE (CC/G-MOLE) *
C * X(I) THE MOLE FRACTION OF COMPONENT I IN THE LIQUID *
C * PHASE *
C * Y(I) THE MOLE FRACTION OF COMPONENT I IN THE GAS OR *
C * SCF PHASE *
C WWW“

DIMENSION ANT(3,3),C(3),DHF(3),FG(3),K(3,3),OMEGA(3),PC(3),PHI(3)

DIMENSION SOLFC(3),TC(3),TM(3),VC(3),VL(3),VS(3),X(3),Y(3),ZRA(3)

INTEGER NS,S

REAL INCR,LV,NEWX(3)

DOUBLE PRECISION ADELTA1,ADELTA2,DELRV,DELTAR,DELTA1,DELTA2,DELX

DOUBLE PRECISION DFG(3),DI,DINCR,DNEWX(3),DP,DP1,DPHI(3),DRATIO(3)

DOUBLE PRECISION DPTOP,DX(3),DXOLD,DY(3),DYNEW,DZ,OLDRV,RV

DOUBLE PRECISION DELRVMIN

OPEN (UNIT - 5, STATUS - 'UNKNOWN')

OPEN (UNIT - 6, STATUS - 'UNKNOWN')

OPEN (UNIT - l7, STATUS - 'NEW', FILE - 'OUTPUT.DAT')

CALL INPUT (ANT,C,DHF,K,NC,0MEGA,PC,PTOT,T,TC,TM,VC,VL,VS,X,Y)

CALL FIXXY (NC,DX,DY,X,Y)

DOLDX - 1.D0

WRITE (6,66)

READ (5,*) T

WRITE (6,68)

READ (5,*) S

IF (S.EQ.2) NS - 3

IF (S.EQ.3) NS - 2

WRITE (6,70)

READ (5,*) DP1

WRITE (6,74)

READ (5,*)DPTOP

WRITE (6,78)

READ (5,*)DINCR

WRITE (17,86)

WRITE (17,90)

DI - DINCR

DP - DP1
C mmm*mmummmmfifi*
C * THE NEXT STATEMENT IS INTENDED TO GIVE A REASONABLE FIRST GUESS *
C * FOR THE FUGACITY OF THE LIGHT COMPONENT FOR THE FIRST ITERATION. *
c **********************************************************************

DFG(I) - DP1

WRITE (6,84)

READ (5,*) RV

OLDRV - RV*2.D0

300

400
410

450

500

50

600

130

DELRV - RV*1.D-01
DELRMIN - -1.D-07
DELTAR - (RV - OLDRV)
OLDRV - RV
DELRV - . 3*DELTAR
IF (ABS(DELRV).LT.DELRMIN) DELRV - DELRMIN
DELTAZ - -lOO.D0
ADELTA2 - DABS(DELTA2)
LOOPS - 1.
CALL SFUG(ANT,DFG,NC,DP,T,VS)
DY(l) - 1.D0 - DY(S)*(1.DO + RV)
DY(NS) - DY(S)*RV
CALL VEOS2(C,DFG,K,NC,OMEGA,DP,PC,DPHI,T,TC,VV,DY,DZ)
DYNEW - DFG(S)/DPHI(S)/DP
DELY - ABS((DYNEW - DY(S))/(DYNEW + DY(S)))
DY(S) - DYNEW
IF (DELY.GE.1.D-4) GOTO 410
DFG(l) - DY(1)*DPHI(1)*DP
DFG(NS) - DY(NS)*DPHI(NS)*DP
CALL LEOS(C,DFG,K,NC,OMEGA,DP,PC,DPHI,T,TC,LV,DX,DZ)
DSUMX - 0.0D0
DO 500 I - 1,NC
DNEWX(I) - DFG(I)/DPHI(I)/DP
DSUMX - DSUMX + DNEWX(I)
CONTINUE
DELX - DABS(DNEWX(1)-DX(l))/DX(1)
DX(l) - (DX(l)+DNEWX(1))/2
IF (DX(l).EQ.DXOLD) THEN

WRITE (6,50)

FORMAT (X,'X(1) NOT CHANGING')
STOP

ENDIF

IF (DX(I).LT.DXOLD) DX(1)-DXOLD
DO 600 JJ-2,NC
DX(JJ) - (1.DO - DX(l))*DNEWX(JJ)/(DSUMX-DX(1))
CONTINUE
IF (DELX.GT.2.5D-4) GOTO 450
DELTAl - DELTA2
DELTA2 - 1.Do - DSUMX
ADELTAI - DABS(DELTAI)
ADELTA2 - DABS(DELTA2)
IF (ADELTA2.GE.1.D-03) THEN
IF (DELTA2 /DELTA1 . LT. O . DO) THEN
DELRV - -DELRV/2.D0
ELSE IF(ADELTA2.GT.ADELTA1) THEN
DELRV - -DELRV/2.DO
ENDIF
Rv - RV + DELRV
LOOPS - LOOPS + 1
IF (LOOPS.GT.SOOO) THEN
WRITE (6,92) DP,T,DX(1),DX(2),DY(1),DY(2)
WRITE (6,93) DELTA2,ADELTA2,DELRV
ENDIF

1000

1200

1300

1310

1320

1330

1340

1350

1360

1500

2000
66
68
7O
74
78
82

131

GOTO aoo
ENDIF
PPSIA - DPTOT*14.696
TDEGC - T - 273.15
DOLDX - DX(I)
WRITE (17,92) DP,T,DX(2),DX(3),DY(2),DY(3)
WRITE (6,94) DP,T,LOOPS
DO 1200 I-1,NC
DRATIO(I) - DY(I)/DX(I)
CONTINUE
1300 I - 2,NC
IF (DRATIO(I)
CONTINUE
1310 I - 2,NC
IF (DRATIO(I)
CONTINUE
1320 I - 2,NC
IF (DRATIO(I)
CONTINUE
1330 I - 2,NC
IF (DRATIO(I)
CONTINUE
1340 I - 2,NC
IF (DRATIO(I)
CONTINUE
1350 I - 2,NC
IF (DRATIO(I)
CONTINUE
1360 I - 2,NC
IF (DRATIO(I).GT.3.5D-Ol)
CONTINUE
(DI.LE.DINCR)
(DP.EQ.DPTOP)
GOTO 2000
ELSE
IF (DP.EQ DP1) THEN
DP - DINCR
IF (DP.GT DP1) GOTO
DP - DP + DINCR
GOTO 1500

DO

.GT.5.0D-02) DI - 5.0

.GT.8.0D-02) DI - 2.5

.GT.1.1D-01) DI - 1.0

.GT.l.3D-01)

.GT.2.0D-01) DI - 0.25

.GT.3.0D-Ol) DI - 0.1

DI - 0.05

DINCR - DI
THEN

IF
IF

300

ELSE
DP - DP + DINCR
IF (DP.GT.DPTOP) DP - DPTOP
GOTO 300
ENDIF
ENDIF
CONTINUE
FORMAT (X,'INPUT TEMPERATURE IN KELVIN (REAL #)')
FORMAT (X,'WHICH COMPONENT FORMS A SOLID PHASE?’)
FORMAT (1X,'INPUT LOWEST PRESSURE IN BAR')
FORMAT (1X,'INPUT HIGHEST PRESSURE IN BAR')
FORMAT (1X,'INPUT THE SIZE OF THE PRESSURE INCREMENT IN BAR')
FORMAT (1X,'INPUT K(',Il,',',Il,')')

CIC)CUCICICIC3C5C)C)C)C3C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C§C)C)C)C)C§

132

84 FORMAT (X,'INPUT INITIAL GUESS FOR Rv')

86 FORMAT (X,'PRESSURE MELTING POINT')

90 FORMAT (X,' (BAR) (K) X2 X3 Y2
& Y3')

92 FORMAT (X,F8.3,2X,Fl3.5,4(2X,G9.4))

93 FORMAT (X,3(G15.8,5X)/)

94 FORMAT (1X,'THE MELTING POINT AT ',F8.3,' BAR IS ',015.7,3X,I5)

96 FORMAT (X,F5.1,F7.2,8(X,G9.3))

 

END

******************************************************************
* SUBROUTINE VEOS2 USING ORIGINAL PENG-ROBINSON EOS *
******************************************************************
* A0 ------ THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC *
* EQUATION TO BE SOLVED *
* A1 ------ THE FIRST ORDER TERM OF THE NORMALIZED CUBIC *
* EQUATION TO BE SOLVED *
* A2 ------ THE SECOND ORDER TERM OF THE NORMALIZED CUBIC *
* EQUATION TO BE SOLVED *
* ASTAR SINGLE PRECISION DASTAR *
* BSTAR SINGLE PRECISION DBSTAR *
* Cl IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC *
* C2 IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC *
* C3 IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC *
* C(I) VOLUME TRANSLATION FOR COMPONENT I - NOT USED IN *
* THIS SUBROUTINE *
* DA(I) PENG-ROBINSON 8 FOR PURE COMPONENT I *
* DAM 8 OF THE MIXTURE *
* DASTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION *
* T0 SOLVE FOR 2 *
* DB(I) PENG-ROBINSON b FOR PURE COMPONENT I *
* DBM b OF THE MIXTURE *
* DBSTAR INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION *
* TO SOLVE FOR 2 *
* DBTERM RATIO DB(I)/DBM, USED IN CALCULATING FUGACITY *
* COEFFICIENT OF COMPONENT I *
* DEL USED IN CALCULATING FUGACITY COEFFICIENTS *
* DELY(I) CHANGE IN VALUE OF DY(I) FROM LAST ITERATION *
* DFG(I) FUGACITY OF COMPONENT I *
* DFOMEG FUNCTION OF OMEGA USED IN CALCULATING DA(I) VALUES *
* DX(I,J) DOUBLE PRECISION K(I,J) *
* DNEWY(I) NEXT GUESS FOR DY(I) *
* DOM(I) DOUBLE PRECISION OM(I) *
* DP TOTAL SYSTEM PRESSURE (BAR) *
* DR DOUBLE PRECISION R *
* DRLT FIRST LOGARITHMIC TERM USED IN CALCULATING *
* FUGACITY COEFFICIENTS *
* DRLT2 SECOND LOGARITHMIC TERM USED IN CALCULATING *
* FUGACITY COEFFICIENTS *
* DT DOUBLE PRECISION T *
* DTC(I) DOUBLE PRECISION TC(I) *
* DTR DOUBLE PRECISION TR *
* *

DY(I)

VAPOR PHASE MOLE FRACTION OF COMPONENT I

133

C * DZ DOUBLE PRECISION Z *
C * I COMPONENT SUBSRIPT *
C * ICNT ITERATATION LOOP COUNTER *
C * J COMPONENT SUBSCRIPT *
C * K(I,J) INTERACTION PARAMETER FOR THE I,J COMPONENT PAIR *
C * NC TOTAL NUMBER OF COMPONENTS *
C * OM(I) PITZER ACENTRIC FACTOR *
C * PC(I) CRITICAL PRESSURE OF COMPONENT I *
C * PHI(I) FUGACITY COEFFICIENT OF COMPONENT I IN THE MIXTURE *
C * R GAS CONSTANT (CC-BAR/MOL-K) *
C * R1 REAL PART OF THE lST ROOT OF THE SOLVED CUBIC *
C * R2 REAL PART OF THE 2ND ROOT OF THE SOLVED CUBIC *
C * R3 REAL PART OF THE 3RD ROOT OF THE SOLVED CUBIC *
C * T SYSTEM TEMPERATURE (KELVIN) *
C * TC(I) CRITICAL TEMPERATURE OF COMPONENT I (KELVIN) *
C * TR REDUCED TEMPERATURE *
C * V VAPOR PHASE MOLAR VOLUME (CC/MOL) OF MIXTURE AT *
C * SYSTEM P AND T *
C * Z VAPOR PHASE COMPRESSIBILITY OF MIXTURE *
C ******************************************************************

SUBROUTINE VEosz (C,DFG,K,NC,OM,DP,PC,DPHI,T,TC,V,DY,D2)

REAL C(3),K(3,3),OM(3),PC(3),TC(3)

DOUBLE PRECISION DA(3),DAM,DASTAR,DB(3),DBM,DBSTAR,DBTERM,DEL

DOUBLE PRECISION DFG(3),DFOMEG,DK(3,3),DOM(3)

DOUBLE PRECISION DP,DPC(3),DPHI(3),DR,DRLNPHI,DRLT,DRLT2,DT

DOUBLE PRECISION DTC(3),DTR,DY(3),DZ

C OPEN (UNIT - 8, STATUS - 'NEW', FILE - 'VEOS.DAT')

R - 83.1439

DR - DBLE(R)

DT - DBLE(T)

DO 20 J - 1,NC
DOM(J) - DBLE(OM(J))
DPC(J) - DBLE(PC(J))
DTC(J) - DBLE(TC(J))
DTR-DT/DTC(J)
DFOMEG-3.7464D-I+-1.54226DO*DOM(J)-2.6992D-1*DOM(J)**2.DO
DA(J) - 4.57240-1*(DR*DTC(J)*(1.DO + DFOMEG*(1.D0 -

& DSQRT(DTR))))**2.DO/DPC(J)
DB(J) - 7.78D-2*DR*DTC(J)/DPC(J)
20 CONTINUE
C *************************************

C * BEGINNING OF LOOP FOR COMPOSITION *
C *************************************
24 DAM-0
DBM-0
DO 30 I - 1,NC
DBM - DBM + DY(I)*DB(I)
D0 25 J - 1,NC
DX(I,J) - DBLE(K(I,J))
DAM-DAM+DY(I)*DY(J)*DSQRT(DA(I)*DA(J))*(1.D0-DK(I,J))
25 CONTINUE

30 CONTINUE
c “WW-ki-

134

* SOLVE CUBIC EOS *
WWW
DASTAR - DAM*DP/(DR*DT)**2
ASTAR - SNGL(DASTAR)
DBSTAR - DBM*DP/DR/DT
BSTAR - SNGL(DBSTAR)
A2 - BSTAR-1.
A1 - ASTAR-BSTAR*(2. + 3.*BSTAR)
A0 - BSTAR*(BSTAR**2 + BSTAR - ASTAR)
CALL CUBIC(A2,A1,AO,R1,R2,R3,C1,C2,C3,IFLAG)
WWWW
* IFLAC - 1 MEANS ONE REAL + TWO COMPLEX *
* - 2 ALL REAL, AT LEAST TWO SAME *
* - 3 THREE DISTINCT REAL ROOTS *
WWW
IF (IFLAG.EQ.1)THEN
2 - R1
ELSE IF (IFLAG.EQ.2) THEN
2 - R1
IF (2.LT.R2) Z-R2
ELSE
2 - R1
IF (Z.LT.R2) Z-R2
IF (2.LT.R3) 2-R3
ENDIF
D2 - DBLE(2)
v - Z*DR*DT/DP
C WWW**H**W
C * CALCULATE VAPOR PHASE FUGACITIES *
C WW*W****************
DRLT - DLOG((2.D0*DZ + DBSTAR*(2.DO + DSQRT(8.DO)))/(2.DO*DZ +
& DBSTAR*(2.D0 - DSQRT(8.DO))))
DRLT2 - DLOG(D2 - DBSTAR)
DO 700 L - 1,NC
DBTERM - DB(L)/DBM
DEL - O.DO
DO 600 LL - 1,NC
DEL - DEL + 2.D0*DY(LL)*DSQRT(DA(L)*DA(LL))*(1.D0 -

00

00000

& DK(L,LL))/DAM
600 CONTINUE
DRLNPHI - DBTERM*(DZ - l.D0) — DRLT2 + DASTAR*(DBTERM -
& DEL)*DRLT/DBSTAR/DSQRT(8.DO)
DPHI(L) - DEXP(DRLNPHI)
700 CONTINUE
RETURN

END

The

.135

following subroutine was substituted for the

corresponding original Peng-Robinson subroutine (above) when

the translated Peng-Robinson equation was used.

curacucucncucucucuc1c:CIC)cacacucacucucucacuczc1c1c1c1cucucucacacucacuczcucacacucucucacucu

WW*W**H**************W****W*****m*

* SUBROUTINE VEOSZ USING TRANSLATED PENG-ROBINSON EOS
******************************************************************

3(-3‘-fl-ifl-X-fifi-fl-fi-fl-‘1'$361-$361-*3Ga-fl-X-X-IFSI-I’fi-X-fi3ifl'fi-I-fi-fl-fl-fi-fl-I-I-

A0 ------ THE ZEROETH ORDER TERM OF THE NORMALIZED CUBIC

ASTAR
BSTAR
Cl

C2

C3
C(I)
DA(I)
DAM
DASTAR

DB(I)
DBM
DBSTAR

DBTERM

DCM
DEL
DELY(I)
DFG(I)
DFOMEG
DK(I,J)
DNEWY(I)
DOM(I)
DP

DR
DRLT

DRLT2

DT
DTC(I)
DTR
DY(I)
DZ

I

EQUATION TO BE SOLVED

THE FIRST ORDER TERM OF THE NORMALIZED CUBIC

EQUATION TO BE SOLVED

THE SECOND ORDER TERM OF THE NORMALIZED CUBIC

EQUATION TO BE SOLVED
SINGLE PRECISION DASTAR
SINGLE PRECISION DBSTAR

IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC
IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC
IMAGINARY PART OF THE lST ROOT OF THE SOLVED CUBIC

VOLUME TRANSLATION FOR COMPONENT I
PENG-ROBINSON a FOR PURE COMPONENT I
a OF THE MIXTURE

INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION

TO SOLVE FOR 2
PENG-ROBINSON b FOR PURE COMPONENT I
b OF THE MIXTURE

INTERMEDIATE VARIABLE USED TO SET UP CUBIC EQUATION

TO SOLVE FOR Z

RATIO DB(I)/DBM, USED IN CALCULATING FUGACITY

COEFFICIENT OF COMPONENT I
0 OF THE MIXTURE
USED IN CALCULATING FUGACITY COEFFICIENTS

CHANGE IN VALUE OF DY(I) FROM LAST ITERATION

FUGACITY OF COMPONENT I

FUNCTION OF OMEGA USED IN CALCULATING DA(I) VALUES

DOUBLE PRECISION K(I,J)

NEXT GUESS FOR DY(I)

DOUBLE PRECISION OM(I)

TOTAL SYSTEM PRESSURE (BAR)

DOUBLE PRECISION R

FIRST LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

SECOND LOGARITHMIC TERM USED IN CALCULATING
FUGACITY COEFFICIENTS

DOUBLE PRECISION T

DOUBLE PRECISION TC(I)

DOUBLE PRECISION TR

VAPOR PHASE MOLE FRACTION OF COMPONENT I
DOUBLE PRECISION Z

COMPONENT SUBSCRIPT

*

H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H

0000000000000000000

20

24

25
3O

fiafifl-X-fl-fl-X'fi-X-fifl-fl-fl-fl-X-I-X-fi-

ICNT

K(I,J)
NC
OM(I)
PC(I)
PHI(I)
R

R1

R2

R3

T
TC(I)
TR

TZ

V

Z

136

ITERATION LOOP COUNTER

COMPONENT SUBSCRIPT

INTERACTION PARAMETER FOR THE I,J COMPONENT PAIR
TOTAL NUMBER OF COMPONENTS

PITZER ACENTRIC FACTOR

CRITICAL PRESSURE OF COMPONENT I

FUGACITY COEFFICIENT OF COMPONENT I IN THE MIXTURE
GAS CONSTANT (CC-BAR/MOL-K)

REAL PART OF THE lST ROOT OF THE SOLVED CUBIC
REAL PART OF THE 2ND ROOT OF THE SOLVED CUBIC
REAL PART OF THE 3RD ROOT OF THE SOLVED CUBIC
SYSTEM TEMPERATURE (KELVIN)

CRITICAL TEMPERATURE OF COMPONENT I (KELVIN)
REDUCED TEMPERATURE

TRUE VAPOR PHASE COMPRESSIBILITY OF MIXTURE
VAPOR PHASE MOLAR VOLUME (CC/MOL) OF MIXTURE AT
SYSTEM P AND T

VAPOR PHASE COMPRESSIBILITY OF MIXTURE

H H H H H H H H H H H H H H H H H H

WWHWWH**WMRMWWWHW*
SUBROUTINE VEOS2 (C,DFG,K,NC,OM,DP,PC,DPHI,T,TC,V,DY,TZ)
REAL 0(3).K(3.3).0M(3).PC(3).TC(3).ZRA(3)
DOUBLE PRECISION DA(3),DAM,DASTAR,DB(3),DBM,DBSTAR,DBTERM,DC(3)
DOUBLE PRECISION DCM,DEL,DFG(3),DFOMEG,DK(3,3),DOM(3)
DOUBLE PRECISION DP,DPC(3),DPHI(3),DR,DRLNPHI,DRLT,DRLT2,DT
DOUBLE PRECISION DTC(3),DTR,DY(3),DZ,TZ
R - 83.1439
DR - DBLE(R)
DT - DBLE(T)
DO 20 J - 1,NC
DC(J) - DBLE(C(J))
DOM(J) - DBLE(OM(J))
DPC(J) - DBLE(PC(J))
DTC(J) - DBLE(TC(J))
DTR-DT/DTC(J)
DFOMEG-3.7464D-1+-1.54226DO*DOM(J)-2.6992D-1*DOM(J)**2.D0
DA(J) - 4.S7240-1*(DR*DTC(J)*(1.DO + DFOMEG*(1.D0 -

&

DSQRT(DTR))))**2.DO/DPC(J)

DB(J) - 7.78D-2*DR*DTC(J)/DPC(J)
CONTINUE
c *************************************

C * BEGINNING OF LOOP FOR COMPOSITION *
c *************************************
DAM - 0.0D0
DBM - 0.0DO
DCM - 0.0D0

DO

30 I - 1,NC

DBM - DBM + DY(I)*DB(I)

DCM - DCM + DY(I)*DC(I)

DO 25 J - 1,NC
DK(I,J) - DBLE(K(I,J))
DAM-DAM+DY(I)*DY(J)*DSQRT(DA(I)*DA(J))*(1.D0-DK(I,J))
CONTINUE

CONTINUE

C
C
C

0¢3(1C)C)

137’

*******************

* SOLVE CUBIC EOS *
*******************

DASTAR - DAM*DP/(DR*DT)**2

ASTAR - SNGL(DASTAR)

DBSTAR - DBM*DP/DR/DT

BSTAR - SNGL(DBSTAR)

A2 - BSTAR-1.

A1 - ASTAR-BSTAR*(2. + 3.*BSTAR)

A0 - BSTAR*(BSTAR**2 + BSTAR - ASTAR)

CALL CUBIC(A2,A1,AO,R1,R2,R3,Cl,C2,C3,IFLAG)

***********************************************
* IFLAC - l MEANS ONE REAL + TWO COMPLEX *

*
*

- 2 ALL REAL, AT LEAST TWO SAME *
- 3 THREE DISTINCT REAL ROOTS *

***********************************************

IF (IFLAG.EQ.1)THEN
z - R1
ELSE IF (IFLAG.EQ.2) THEN
2 - R1
IF (2.LT.R2) 2-R2
ELSE
z - R1
IF (2.LT.R2) 2-R2
IF (2.LT.R3) 2-R3
ENDIF
Dz - DBLE(2)
T2 - D2 - DCM*DP/DR/DT
V - TZ*DR*DT/DP

C ************************************

C * CALCULATE VAPOR PHASE FUGACITIES *
c ************************************

600

700

DRLT - DLOG((2.D0*DZ + DBSTAR*(2.DO + DSQRT(8.D0)))/(2.D0*DZ +
DBSTAR*(2.D0 - DSQRT(8.D0))))
DRLT2 - DLOG(D2 - DBSTAR)
DO 700 L - 1,NC
DBTERM - DB(L)/DBM
DEL - o.DO
DO 600 LL - 1,NC
DEL - DEL + 2.D0*DY(LL)*DSQRT(DA(L)*DA(LL))*(1.D0 -
DK(L,LL))/DAM
CONTINUE
DRLNPHI - DBTERM*(DZ - 1.DO) - DRLT2 + DASTAR*(DBTERM -
DEL)*DRLT/DBSTAR/DSQRT(8.DO) - DC(L)*DP/DR/DT
DPHI(L) - DEXP(DRLNPHI)
CONTINUE
RETURN
END

APPENDIX G

EQUATION OF STATE PARAMETER DETERMINATIONS

The values of most of the parameters used for the phase
equilibria modeling were taken from existing references. The
values of the parameters and the sources they were obtained
from are tabulated in the data files of Appendix D. The
critical pressure value reported for phenanthrene in a
literature search was originally estimated by the method of
Lydersen with an expected accuracy of t 10%. In light of this
degree of uncertainty, for the calculations in this work, the
value used for the critical pressure of phenanthrene was
optimized to minimize the sum of the squares of the errors for
a fit to the liquid vapor pressure curve from the triple point
to about 50 K below the critical temperature. The optimized
Pc (critical pressure) was 27.43 bar compared to 29.0 bar from
the Lydersen method estimate. This is within the stated range
of accuracy for the correlation value. The acentric factor
was calculated simultaneously for each guess of the Pc value
and using the known values for the vapor pressure and critical
temperature of phenanthrene. Values of the pure component

c-‘s for the translated equation were obtained by translating

1
at the triple points of the pure components. The kij
parameters for the C02+hydrocarbon.binary systems were chosen
to fit the predicted P-T traces to match the measured traces

as closely as possible. Increasing the kij values caused the

138

139
predicted melting points to increase and caused the melting
point curve to bend back more sharply at higher pressures.
Decreasing the kij values caused the predicted melting points
to decrease and caused the melting point curve to bend back
less: at low enough values for the C02/solid interaction
parameters, the melting point curves fail to have any minimum
(i.e. the melting point temperature continue to decrease until
the upper critical end point is reached). The solid/solid
interaction parameters were chosen to improve the fit of the
model to the ternary melting point depression data. The
interaction parameters were optimized independently for the

Peng-Robinson and translated Peng-Robinson equations of state.

The values chosen were:

 

Binarv k°j_23 313.123
C02/biphenyl 0.100 .095
C02/naphthalene 0.109 0.116
COZ/phenanthrene 0.110 0.175
biphenyl/naphthalene —0.02 -0.020
naphthalene/phenanthrene 0.0 -0.008

Figures 6.1 to 6.6 demonstrate the effect of changing the
value of kij has on the P-T traces and liquid mole fractions
predicted by the Peng-Robinson equation of state. The data of
Cheong et al. (1986) and Zhang and Lu (1988) and the
corresponding predictions by the translated Peng-Robinson
equation are also shown for comparison. Increasing kij causes
the P-T trace to bend back more and increases the predicted
mole fraction of the solid in the liquid. Varying kij in the

translated equation has the same effect.

 

 

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(.20 Iml F

RAW COMPOSITION DATA

APPENDIX E

Naphthalene/CO2 SAMPLES AT 67.6’C AND 990 PSIA

V C02 7.9
T 295.35
P (mbar) 976.5
n2 .0003141
n1 .0000052
Y1 .0164296
V C02 3.4
T 302.65
P (mbar) 982.5
n2 .0001328
n1 .0002096
x1 .6122554

7.1
296.15
977
.0002817
.0000010
.0033620

3.5
303.55
981
.0001360
.0002004
.5956496

16.2
297.15
988
.0006478
.0000022
.0033371

3.9
298.15
994
.0001564
.0000175
.1008058

15.9
297.15
988
.0006358
.0000014
.0022516
1.95 3.15
300.65 300.55
985 986
.0000768 .0001243
.0001838 .0001679
.7051679 .5746179

Naphthalene/C02 SAMPLES AT 60.3'C AND 1860 PSIA

V C02 19.2
T K 305.15
P (mbar) 983
n2 .0007439
n1 .0000310
y1 .0399596
V 002 6.7
T K 302.45
P (mbar) 989
n2 .0002635
n1 .0002376
x1 .4741195

28.9
305.15
984
.0011209
.0000172
.0151443

5.35
300.85
984.5
.0002106
.0002334
.5256883

146

30.6
303.85
986
.0011943
.0000152
.0125646

4.25
299.05
987
.0001687
.0002333
.5803339

28.9
303.7
989
.0011319
.0000167
.0145349

4.85
300.05
987
.0001919
.0002339
.5493904

147

Naphthalene/C02 SAMPLES AT 59.2'C AND 2060 PSIA

V CC
T K 2
P (mbar)

34.6
301.15
990
.0013680
.0000317
.0226256

4.95
303.15
996
.0001956
.0002089
.5164461

36
302.15
996
.0014273
.0000349
.0238798

16.1
301.55
990
.0006357
.0000418
.0616995

35.1
302.75
994
.0013861
.0000316
.0223050

19.75
300.85
988.5
.0007805
.0002493
.2420597

34.8
302.95
994
.0013733
.0000330
.0234720

14.05
300.45
988.5
.0005560
.0000334
.0566894

Naphthalene/C02 SAMPLES AT 58.9'C AND 2310 PSIA

v C02 36.25 36.7 37 34.7 30.7
T K 302.05 303.85 303.05 300.25 300.4
P (mbar) 985.5 979 976 984.5 982
n2 .0014225 .0014222 .0014332 .0013685 .0012070
n1 .0000090 .0000683 .0000564 .0000892 .0001370
Y1 .0062721 .0457978 .0378335 .0612223 .1018996
v C02 6.65 7.95 4.8
T K 300.15 300.45 299.65
P (mbar) 989 984 988
n2 .0002635 .0003132 .0001904
n1 .0002384 .0002333 .0001733
x1 .4749060 .4268998 .4764898

Naphthalene/C02 SAMPLES AT 59.2'C AND 3060 PSIA

VCO
2
T 'C

36.2
24.6
297.75
992
.0014506
.0001385
.0871762

17.8
25
298.15
993

.0007130

.0000172
.0236169

29.7

25
298.15
992
.0011885
.0002724
.1864481

35.7
25.9
299.05
990.5
.0014222
.0000721
.0482565

 

148

Naphthalene/C02 SAMPLES AT 59.5’C AND 3220 PSIA

V CC
2
T 'C
T K
P (mbar)

10.15
23.8
296.95
971.5
.0003994
.0000817
.1697813

10.4
23.75
296.9

970
.0004087
.0002002
.3287950

38.6

24
297.15
972
.0015186
.0001217
.0742057

37.45
25.4
298.55
981
.0014800
.0003528
.1924657

9.75
25.1
298.25
973
.0003826
.0000731
.1604873

37.4
24.3
297.45
985
.0014896
.0003249
.1790669

10.3
25.5
298.65
973
.0004036
.0000787
.1631413

39.45
25.3
298.45
973
.0015469
.0001143
.0687821

Naphthalene/C02 SAMPLES AT 59.2'C AND 3060 PSIA

V CO
2
T K

10.4
298.45
979
.0004103
.0001746
.2985180

33.95
298.15
988
.0013531
.0002062
.1322403

10.5
298.95
988
.0004174
.0001742
.2944604

37.6
298.05
987
.0014976
.0001125
.0698925

9.75
299.05
988.5
.0003876
.0001784
.3151282

37.55
298.25
987
.0014946
.0001224
.0756983

10
299.25
988.5
.0003973
.0001803
.3121935

30.4
298.15
987.5
.0012110
.0001364
.1012106

Naphthalene/C02 SAMPLES AT 60.2'C AND 1860 PSIA

V C0
2
T K

17.8
298.15
993
.0007130
.0002327
.2460513

149

Naphthalene/C02 SAMPLES AT 59.7'C AND 3620 PSIA

V CO
2
T K

34.2
296.35
973
.0013505
.0000266
.0193117

11.6
300.45
982
.0004560
.0001673
.2683557

30
299.45
974
.0011736
.0002627
.1828982

12
299.65
979
.0004715
.0001676
.2622537

33.05
299.05
972.5
.0012927
.0001939
.1304249

12.3
299.45
977
.0004827
.0001617
.2509556

28
299.05
970
.0010923
.0003062
.2189216

12.35
299.05
975.5
.0004845
.0001537
.2408517

Biphenyl/C02 SAMPLES AT 58.3'C AND 630 PSIA

V C02 5 4.9 4.9 1.15 2.15
T 'C 23.4 23.3 23.35 23 23.25
T K 296.55 296.45 296.5 296.15 296.4
P (mbar) 993.5 996 995.5 999 999.5
n2 .0002015 .0001980 .0001979 .0000467 .0000872
n1 .0000039 .0000025 .0000015 .0001269 .0000089
y1 .0187998 .0122260 .0075816 .7310929 .0926092
V C02 5.1 2.1 2.05
T 'C 25.5 23.2 23.4
T K 298.65 296.35 296.55
P (mbar) 980 999 999.5
n2 .0002013 .0000851 .0000831
n1 .0000133 .0000087 .0000122
x1 .0619944 .0924913 .1281251

Biphenyl/C02 SAMPLES AT 48.65‘C AND 1400 PSIA

V CO
2
T K

36.2
297.75
992
.0014506
.0000212
.0143832

17.8
298.15
993
.0007130
10.31381
.9999309

30.7
300.4
982
.0012070
.0000042
.0034539

34.7
300.25
984.5
.0013685
.0000013
.0009380

150

Naphthalene/Biphenyl Ternary at 410 psia and 42.20 'C

HOLES N .0000003 .0000030 3.8223-8
HOLES B .0000012 .0000101 .0000002

ml GAS 4.3 6.3 3
P (mbar) 978 1001 1001
T R 296.95 294.15 294.55

HOLES CO .0001703 .0002579 .0001226
TOTAL MO .0001719 .0002710 .0001229

y N .0018001 .0110240 .0003110
y B .0072236 .0374451 .0019849

HOLES N .0000887 .0000962
HOLES B .0002158 .0002376

ml GAS 1.9 1.6
P (mbar) 986 982
T K 301.35 301.35

HOLES CO .0000748 .0000627
TOTAL HO .0003792 .0003965

x N .2338357 .2426674
x B .5689920 .5991919
Naphthalene/Biphenyl Ternary at 1070

HOLES N .0000070 .0000067 .0000066
HOLES B .0000126 .0000072 .0000094

ml GAS 38.5 38.2 38.9
P (mbar) 983 982 982
T K 295.55 295.55 295.55

HOLES CO .0015401 .0015266 .0015545
TOTAL MO .0015597 .0015405 .0015705

y N .0044871 .0043737 .0041860
y B .0080567 .0046523 .0059753

HOLES N .0000550 .0000969 .0000859
HOLES B .0001526 .0002367 .0002235

ml GAS 5 5.7 5.7
P (mbar) 982.5 984 975
T K 294.95 295.55 295.35

HOLES CO .0002003 .0002282 .0002263
TOTAL MO .0004079 .0005618 .0005357

x N .1348403 .1724022 .1604208
x B .3740594 .4213144 .4171199

.0000001 .0000004
.0000074 .0000001

3.2 4.4

1001 979
294.35 301.35
.0001309 .0001719
.0001385 .0001724

.0010727 .0022143
.0537719 .0004481

psia and 32.65 'C

.0000057
.0000085
37.75
976
295.45
.0014999
.0015141

.0037845
.0055918

.0000752
.0001973
5.5

975
295.25
.0002184
.0004910

.1532426
.4018509

 

151

Naphthalene/Biphenyl Ternary at 760 psia and 52.80 'C

HOLES N
HOLES B
ml GAS

P (mbar)
T 'C

T K
HOLES CO
TOTAL HO

yN
yB

HOLES N
HOLES B
ml GAS

P (mbar)
T 'C

T K
HOLES C0
TOTAL HO

x N
KB

.0000003
.0000005
5.7

992
23.6
296.75
.0002292
.0002300

.0013907
.0022198

.0002384
.0000897
2.4

989

22.9
296.05
.0000964
.0004245

.5616530
.2112060

.0000047
.0000019
5.7

986

22.9
296.05
.0002283
.0002350

.0199467
.0082989

.0002335
.0000354
2.4

990

23
296.15
.0000965
.0003654

.6390803
.0968728

.0000003
.0000001
5.8
986.5
23.4
296.55
.0002321
.0002324

.0013185
.0003153

.0002213
.0000860
2.45
986
23.6
296.75
.0000979
.0004052

.5461984
.2121431

Naphthalene/Biphenyl Ternary at 1180

HOLES N
HOLES B
ml GAS

P (mbar)
T K
HOLES CO
TOTAL HO

HOLES CO
TOTAL MO

x N
x B

0

0

38.7

979
300.25
.0015177
0

0
0

.0001861
.0000853
6.9

984
297.25
.0002747
.0005462

.3408213
.1561708

0

O

36.6

978
300.25
.0014339
0

O
0

.0001979
.0000358
6.6

979
299.75
.0002593
.0004929

.4014298
.0725979

0

0

38.8
976.5
300.25
.0015177
0

O
0

.0000002
.0000001
5.6

986
23.9
297.05
.0002236
.0002238

.0007561
.0004202

.0002377
.0000909
2.3

986
23.6
296.75
.0000919
.0004206

.5652421
.2162126

psia and 42.20 ’C

152

Naphthalene/Biphenyl Ternary at 780 psia and 32.65 'C

HOLES N
HOLES B
m1 GAS

P (mbar)
T 'C

T K
HOLES CO
TOTAL H0

T K
HOLES CO
TOTAL MO

x N
x B

.0000002
.0000002
6.3

986

23.3
296.45
.0002520
.0002524

.0008844
.0006461

.0001056
.0002150
3.25

981

22
295.15
.0001299
.0004506

.2344290
.4772334

.0000002
.0000003
6.1

987

23.2
296.35
.0002443
.0002448

.0007259
.0010683

.0000988
.0002068
2.9

981

23.4
296.55
.0001154
.0004210

.2345902
.4913301

.0000001
.0000001
7.1
982.5
23.3
296.45
.0002830
.0002833

.0003567
.0005155

.0000074
.0000150
2.3

981

23.4
296.55
.0000915
.0001139

.0650834
.1315398

Naphthalene/Biphenyl Ternary at 1080

HOLES N
HOLES B
m1 GAS

P (mbar)
T K
HOLES CO
TOTAL HO

y N
Y B

HOLES N
HOLES B
ml GAS

P (mbar)
T K
HOLES CO
TOTAL H0

X N
X B

.0000146
.0000070
36.6

985
296.5
.0014624
.0014840

.0098458
.0047249

.0001516
.0001324
5

984
296.45
.0001996
.0004836

.3134186
.2737992

.0000137
.0000066
36.4
985.5
296.45
.0014554
.0014757

.0093007
.0044559

.0001631
.0001368
5.4

984
296.45
.0002156
.0005155

.3164753
.2653291

.0000049
.0000024
24.9
985.5
296.35
.0009959
.0010032

.0048765
.0024031

.0001653
.0001347
5.7

984
296.35
.0002276
.0005277

.3133110
.2553180

.0000001
.0000001
7.1

983

23.3
296.45
.0002832
.0002833

.0002270
.0003651

.0000661
.0001263
3.05
981.5
23.4
296.55
.0001214
.0003138

.2105704
.4025639

.0000986
.0002034
3.05

983

23.3
296.45
.0001216
.0004236

.2327820
.4800779

psia and 32.65 'C

.0000046
.0000021
24.65
986
296.45
.0009861
.0009928

.0046034
.0021353

.0001702
.0001319
5.9

985
296.45
.0002358
.0005379

.3164466
.2452202

.0000062
.0000030
23.55
987
296.45
.0009430
.0009522

.0064661
.0031917

 

153

Naphthalene/Biphenyl Ternary at 920 psia and 32.65 'C

HOLES N
HOLES B
ml GAS
P (mbar)
T K

HOLES CO

TOTAL MO

y N
y B

HOLES N
HOLES B
m1 GAS

P (mbar)
T K
HOLES C0
TOTAL HO

x N
X B

.0000027
.0000023
9.6

986
296.65
.0003838
.0003888

.0068918
.0059256

.0001492
.0001620
3.3

988
297.15
.0001320
.0004431

.3365973
.3655872

.0000025
.0000021
9.6

987
297.15
.0003835
.0003881

.0063497
.0055100

.0000018
.0000016
4.4
987.5
296.05
.0001765
.0001800

.0101909
.0089817

.0000003
.0000024
9.7
987.5
296.15
.0003890
.0003917

.0006450
.0061550

.0000002
.0000024
4.8
987.5
296.25
.0001924
.0001951

.0011540
.0124725

.0000002
.0000002
9.9
987.5
296.05
.0003972
.0003976

.0006216
.0004148

.0001608
.0001493
3.95

987
296.05
.0001584
.0004686

.3432574
.3187095

.0000004
.0000005
9.8
987.5
296.1
.0003931
.0003940

.0010928
.0011683

.0001688
.0001560
3.75
987.5
296.05
.0001504
.0004752

.3551726
.3282578

154

Naphthalene/Biphenyl Ternary at 920 psia and 32.65 'C
(continued)

HOLES N .0001698 .0001658
HOLES B .0001552 .0001536

ml GAS 3.9 4.2
P (mbar) 987 988
T K 295.95 295.9

HOLES CO .0001564 .0001687
TOTAL HO .0004814 .0004881

x N .3526569 .3397802
x 8 .3223811 .3146356

 

BIBLIOGRAPHY

BIBLIOGRAPHY

Adachi, Y., H. Sugie, and B. C.-Y. Lu, Fluid Phase Equilib.,
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